{"id":1633,"date":"2022-04-21T09:30:20","date_gmt":"2022-04-21T09:30:20","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1633"},"modified":"2024-04-02T04:57:57","modified_gmt":"2024-04-02T04:57:57","slug":"parallel-and-perpendicular-lines-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines","title":{"rendered":"Parallel and Perpendicular Lines &#8211; Definition With Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-f5658634-8f7d-41d2-90e3-a9d81d94276e\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#0-what-are-parallel-and-perpendicular-lines>What Are Parallel and Perpendicular Lines?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#4-properties-of-parallel-and-perpendicular-lines>Properties of Parallel and Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#7-difference-between-parallel-and-perpendicular-lines>Difference between Parallel and Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#11-solved-examples-on-parallel-and-perpendicular-lines>Solved Examples on Parallel and Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#12-practice-problems-on-parallel-and-perpendicular-lines>Practice Problems on Parallel and Perpendicular Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines#13-frequently-asked-questions-on-parallel-and-perpendicular-lines>Frequently Asked Questions on Parallel and Perpendicular Lines<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-parallel-and-perpendicular-lines\">What Are Parallel and Perpendicular Lines?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Parallel and perpendicular lines are two important concepts in geometry. Parallel lines are the lines that never intersect each other. Thus, two parallel lines always maintain a constant distance between them. Perpendicular lines are the two lines that intersect each other at a right angle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We come across examples of parallel lines and perpendicular lines in daily life. Observe the white lines or stripes in a marked crosswalk. They represent parallel lines. When an analog clock reads 03:00, the minute hand and the hour hand of the clock represent perpendicular lines since they make a right angle (90\u00b0 angle).<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions-using-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_upto_1_nl_pt.png\" alt=\"Add Like Fractions using Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions using Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-pairs-of-parallel-sides-in-shapes-and-choose-the-correct-answer\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_parallel_2d_shape_pt.png\" alt=\"Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/divide-using-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_divide_nl_pt.png\" alt=\"Divide using Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Divide using Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-parallel-sides\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_sides_1_pt.png\" alt=\"Find Parallel Sides Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Parallel Sides Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-fractions-on-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_identify_fraction_nl_pt.png\" alt=\"Identify Fractions on Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Fractions on Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-kite-rhombuses-and-parallelograms\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_rhombus_parallelogram_pt.png\" alt=\"Identify Kite, Rhombuses and Parallelograms Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Kite, Rhombuses and Parallelograms Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-lines-line-segments-rays-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_pt_line_ray_angle_pt.png\" alt=\"Identify Lines, Line Segments, Rays, Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Lines, Line Segments, Rays, Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-parallel-and-perpendicular-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_types_of_lines_pt.png\" alt=\"Identify Parallel and Perpendicular Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel and Perpendicular Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-parallel-sides\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_sides_2_pt.png\" alt=\"Identify Parallel Sides Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel Sides Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-parallel-sides-in-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_2d_shape_pt.png\" alt=\"Identify Parallel Sides in Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel Sides in Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    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         }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-parallel-and-perpendicular-lines\">Definition of Parallel and Perpendicular Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Parallel and perpendicular lines play a vital role in geometry. Both of them have distinct properties and applications.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-definition-of-parallel-lines\">Definition of Parallel Lines<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Two lines are said to be parallel if they lie in the same plane and the distance between them is the same. Parallel lines never meet each other. We use the symbol || for parallel lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the lines AB and CD are parallel, we represent them as $AB\\; || \\;CD$.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-definition-of-perpendicular-lines\">Definition of Perpendicular Lines<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Two lines are said to be perpendicular if they are intersecting and always meet at an angle of 90\u00b0. We use the symbol $\\bot$ to represent the perpendicular lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the lines PQ and RS are perpendicular, we write $PQ\\; \\bot \\;RS$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s take a look at the visual examples of perpendicular lines and parallel lines!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"457\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-and-perpendicular-lines-examples.png\" alt=\"Parallel and perpendicular lines examples\" class=\"wp-image-41420\" title=\"Parallel and perpendicular lines examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-and-perpendicular-lines-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-and-perpendicular-lines-examples-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-properties-of-parallel-and-perpendicular-lines\">Properties of Parallel and Perpendicular Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s discuss a few important properties of parallel and perpendicular lines.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-properties-of-parallel-lines\">Properties of Parallel Lines<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Parallel lines are always at an equal or same distance from each other.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Parallel lines never meet even after they are extended infinitely.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">They have the same slope.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-properties-of-perpendicular-lines\">Properties of Perpendicular Lines<\/h3>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Perpendicular lines always intersect at an angle of $90^{\\circ}$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">All perpendicular lines are intersecting lines, but all intersecting lines are not perpendicular because they need to intersect at right angles.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The product of slopes of two perpendicular lines is $-1$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-difference-between-parallel-and-perpendicular-lines\">Difference between Parallel and Perpendicular Lines<\/h2>\n\n\n\n<figure class=\"wp-block-table is-style-regular eplus-wrapper\"><table class=\"has-base-3-background-color has-background has-fixed-layout\"><thead><tr><th><strong>Parallel Lines<\/strong><\/th><th><strong>Perpendicular Lines<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Parallel lines never intersect each other. They are non-intersecting lines.<\/td><td>Perpendicular lines are two intersecting lines. They intersect each other at right angles.<\/td><\/tr><tr><td>We denote parallel lines by the symbol $||$.<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$AB\\; || \\;CD$<\/td><td>We denote perpendicular lines by the symbol $\\bot$.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$AB \\bot CD$<\/td><\/tr><tr><td>The slopes of parallel lines are equal.<\/td><td>The product of slopes of two perpendicular lines is $-1$.<\/td><\/tr><tr><td>Examples: Tram tracks, Vertical lines in the letter <strong>H<\/strong><\/td><td>Examples: Horizontal line and vertical line in the letter <strong>T, <\/strong>Hands of a clock when the analog clock reads 09:00<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-equations-of-parallel-and-perpendicular-lines\">Equations of Parallel and Perpendicular Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We represent a straight line through an equation $y = mx + c$ where \u201cm\u201d represents the slope of the line and c is the y-intercept. Two parallel lines never intersect each other and have the same steepness, so their slopes are always equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider two lines&nbsp; $y = 2x\\; &#8211; \\;1$ and&nbsp; $y = 2x + 3$. We can see that both the equations have the same slope, 2. In mathematical terms, we can express it as $m_1 = m_2 = 2$, where $m_1$ and $m_2$ are the slopes of the lines.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"695\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-lines-on-coordinate-plane.png\" alt=\"Parallel lines on coordinate plane\" class=\"wp-image-41421\" title=\"Parallel lines on coordinate plane\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-lines-on-coordinate-plane.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/parallel-lines-on-coordinate-plane-268x300.png 268w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The slopes of perpendicular lines are not the same. The slope of one line is the negative reciprocal of the other line. In other words, their product is $-1$. We can mathematically express it as $m_1 \\times m_2 = \\;-1$, where $m_1$ and $m_2$ are the slopes of two perpendicular lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose we have a two lines $y = 2x +3$ and $y = \\;-\\frac{1}{2}x \\;-\\; 1$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, $m_1 = 2$ and&nbsp; $m_2 = \\;-\\;\\frac{1}{2}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $m_1 \\times m_2 = \\;-1$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s plot these perpendicular lines on a graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\" id=\"Perpendicular-lines-on-coordinate-plane\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"491\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perpendicular-lines-on-coordinate-plane.png\" alt=\"Perpendicular lines on coordinate plane\" class=\"wp-image-41422\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perpendicular-lines-on-coordinate-plane.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/perpendicular-lines-on-coordinate-plane-300x238.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>In summary:&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If the slopes of two lines are the same, they are parallel lines.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">if the slopes of two given lines are negative reciprocals of each other, they are perpendicular lines.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"9-writing-equations-of-parallel-lines\">Writing Equations of Parallel Lines<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose we have a line whose equation is $y = 4x \\;-\\;3$ and the point on the other line parallel to it is $(2,\\;12)$. Here, slopes $m_1 = m_2 = 4$ as the lines are parallel.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that equation of line with slope m is $y = m_2 x + c$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the values of $(x,\\;y)$ and m, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$12 = 8 + c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$c = 12 \\;-\\; 8 = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the equation of line parallel to $y = 4x \\;-\\; 3$ is $y = 4x +4$.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"10-writing-equations-of-perpendicular-lines\">Writing Equations of Perpendicular Lines<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose we have a line whose equation is $y = 3x + 2$ and the point on the other line parallel to it is (0,1). Here, slopes $m_1 \\times m_2 = \\;-\\;1$ as the lines are perpendicular.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m_2 = \\frac{-1}{m_1} = \\frac{-1}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that equation of line with slope m is $y = m_2 x + c$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the values of $(x,\\;y)$ and $m_2$, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1 = \\frac{-1}{3} \\times 0 + c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$c = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the equation of line perpendicular to $y = 3x +2$ is $y = \\frac{-1}{3} x + 1$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-solved-examples-on-parallel-and-perpendicular-lines\">Solved Examples on Parallel and Perpendicular Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1<\/strong>. <strong>Which triangle has perpendicular lines in it?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>Right-angled triangle has perpendicular lines in it.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"242\" height=\"243\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/right-angled-triangle.png\" alt=\"Right-angled triangle\" class=\"wp-image-41423\" title=\"Right-angled triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/right-angled-triangle.png 242w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/right-angled-triangle-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/right-angled-triangle-120x120.png 120w\" sizes=\"auto, (max-width: 242px) 100vw, 242px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. If the slope of one of the two parallel lines is 5, then what will be the slope of the other parallel line?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> $m_1 = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the slopes of two parallel lines are equal, i.e., $m_1 = m_2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $m_2 = 5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Find the slopes of the lines <\/strong>&nbsp;$5x + 2y\\;-\\;6 = 0$ and $-2x + 5y + 3 = 0$.<strong> Also, which types of lines are they?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>Converting both the equations in slope intercept form, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5x + 2y\\;-\\;6 = 0 \\Rightarrow 2y = \\;-\\;5x + 6y = \\frac{-5}{2} x + 3$. So, $m_1 = \\frac{-5}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$ &#8211; 2x + 5y + 3 = 0 \\Rightarrow 5y = 2x\\;-\\;3 \\Rightarrow y = \\frac{2}{5}x\\;-\\;\\frac{3}{5}$. So, $m_2 = \\frac{2}{5}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m_1 \\times m_2 = \\frac{\\;-\\;5}{2} \\times \\frac{2}{5} = \\;-\\;1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The lines are perpendicular.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. State true and false for the following statements. Also, give reason.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>a.) The letter V has a set of parallel lines.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>b.) The adjacent sides of a square are parallel lines.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>c.) Perpendicular lines intersect each other at <\/strong>$90^\\circ$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> V has intersecting lines as they meet each other. They are not perpendicular. Hence, (a) is false.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The angle between the adjacent sides of the square is $90^\\circ$ which means adjacent sides are perpendicular. Hence, (b) is false.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(c) is true as the angle between perpendicular lines is $90^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. If two lines are parallel to each other and equation of one line is <\/strong>$y = \\;-\\;7x + 3$<strong> and the point on the other line is <\/strong>$(2,-5)$<strong>, then what will be the equation of the other line?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Slope of $y = \\;-\\;7x + 3$ is $m_1 = \\;-7$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since, the lines are parallel, so $m_1 = m_2 = \\;-7$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that equation of line with slope $m$ is $y = m_2\\; x +c$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the values of $(x,\\;y)$ and m, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$-5 = \\;-7 \\times 2 + c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$c = \\;-5 + 14 = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The equation will be: $y = \\;-7x + 9$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-practice-problems-on-parallel-and-perpendicular-lines\">Practice Problems on Parallel and Perpendicular Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Parallel and Perpendicular Lines - Definition With Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following is an example of parallel lines?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Adjacent sides of a rectangle<\/div><div class=\"spq_answer_block\" data-value=\"1\">Sides of an Equilateral Triangle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Plus sign<\/div><div class=\"spq_answer_block\" data-value=\"3\">Opposite sides of a paralleogram<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Opposite sides of a paralleogram<br\/>The opposite sides of a parallelogram are parallel to each other.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following letters is not an example of perpendicular lines?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">L<\/div><div class=\"spq_answer_block\" data-value=\"1\">T<\/div><div class=\"spq_answer_block\" data-value=\"2\">N<\/div><div class=\"spq_answer_block\" data-value=\"3\">H<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: N<br\/>L, T and H are the examples of perpendicular lines. N has no perpendicular lines.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If the slope of one of the perpendicular line is $\\frac{-3}{4}$, then what will be the slope of the other perpendicular line?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{-3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{-4}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{3}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{4}{3}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{4}{3}$<br\/>The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $= \\frac{4}{3}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which word best describes the lines  $3x + 4y \\;-\\; 6 = 0$ and $12x + 16y +9 = 0$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Intersecting<\/div><div class=\"spq_answer_block\" data-value=\"1\">Perpendicular<\/div><div class=\"spq_answer_block\" data-value=\"2\">Parallel<\/div><div class=\"spq_answer_block\" data-value=\"3\">Adjacent<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Parallel<br\/>$3x + 4y \\;-\\; 6 = 0 \\Rightarrow 4y = \\;-\\; 3x + 6 \\Rightarrow y = \\frac{-3}{4} + \\frac{6}{4}$. So,  $m_1 = \\frac{-3}{4}$.<br>\r\n$12x + 16y + 9 = 0 \\Rightarrow 16y = \\;-\\;12x\\;-\\;9 \\Rightarrow y = \\frac{-12}{16}\\;-\\;\\frac{9}{16}$. So, $m_2 = \\frac{-12}{16} = \\frac{-3}{4}$.<br>\r\n$m_1 = m_2$.<br>\r\nHence, the lines are parallel.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">If two lines are perpendicular, then which of the following is true?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">They never intersect with each other.<\/div><div class=\"spq_answer_block\" data-value=\"1\">The slope of them are negative reciprocals of each other.<\/div><div class=\"spq_answer_block\" data-value=\"2\">Their slopes are equal.<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: The slope of them are negative reciprocals of each other.<br\/>If two lines are perpendicular, the slope of them are negative reciprocals of each other.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Parallel and Perpendicular Lines - 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N has no perpendicular lines.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"T\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"L, T and H are the examples of perpendicular lines. N has no perpendicular lines.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"H\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"L, T and H are the examples of perpendicular lines. 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N has no perpendicular lines.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the slope of one of the perpendicular line is $$\\\\frac{-3}{4}$$, then what will be the slope of the other perpendicular line?\",\n                    \"text\": \"If the slope of one of the perpendicular line is $$\\\\frac{-3}{4}$$, then what will be the slope of the other perpendicular line?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{-3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{-4}{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{4}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The slopes of a perpendicular line are the negative reciprocal of another perpendicular line.<br>\r\nSo, slope of other line $$= \\\\frac{4}{3}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which word best describes the lines  $$3x + 4y \\\\;-\\\\; 6 = 0$$ and $$12x + 16y +9 = 0$$.\",\n                    \"text\": \"Which word best describes the lines  $$3x + 4y \\\\;-\\\\; 6 = 0$$ and $$12x + 16y +9 = 0$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Intersecting\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Perpendicular\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Adjacent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Parallel\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$3x + 4y \\\\;-\\\\; 6 = 0 \\\\Rightarrow 4y = \\\\;-\\\\; 3x + 6 \\\\Rightarrow y = \\\\frac{-3}{4} + \\\\frac{6}{4}$$. So,  $$m_1 = \\\\frac{-3}{4}$$.<br>\r\n$$12x + 16y + 9 = 0 \\\\Rightarrow 16y = \\\\;-\\\\;12x\\\\;-\\\\;9 \\\\Rightarrow y = \\\\frac{-12}{16}\\\\;-\\\\;\\\\frac{9}{16}$$. So, $$m_2 = \\\\frac{-12}{16} = \\\\frac{-3}{4}$$.<br>\r\n$$m_1 = m_2$$.<br>\r\nHence, the lines are parallel.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If two lines are perpendicular, then which of the following is true?\",\n                    \"text\": \"If two lines are perpendicular, then which of the following is true?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"They never intersect with each other.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Their slopes are equal.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"The slope of them are negative reciprocals of each other.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If two lines are perpendicular, the slope of them are negative reciprocals of each other.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-frequently-asked-questions-on-parallel-and-perpendicular-lines\">Frequently Asked Questions on Parallel and Perpendicular Lines<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-328e7d00-6dda-4d62-b6d2-302791c40cf8\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-328e7d00-6dda-4d62-b6d2-302791c40cf8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-328e7d00-6dda-4d62-b6d2-302791c40cf8\"><strong>What is the difference between parallel lines and intersecting lines?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-328e7d00-6dda-4d62-b6d2-302791c40cf8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Parallel lines are the lines which never intersect each other even if we extend them infinitely whereas intersecting lines meet each other at a point.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-328e7d00-6dda-4d62-b6d2-302791c40cf8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-328e7d00-6dda-4d62-b6d2-302791c40cf8\"><strong>Are all intersecting lines perpendicular?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-328e7d00-6dda-4d62-b6d2-302791c40cf8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No. Intersecting lines can meet at any angle. But all perpendicular lines are intersecting lines.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-328e7d00-6dda-4d62-b6d2-302791c40cf8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-328e7d00-6dda-4d62-b6d2-302791c40cf8\"><strong>What common characteristics do parallel and perpendicular lines have?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-328e7d00-6dda-4d62-b6d2-302791c40cf8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The common characteristic is that both have straight lines.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-328e7d00-6dda-4d62-b6d2-302791c40cf8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-328e7d00-6dda-4d62-b6d2-302791c40cf8\"><strong>Can a figure have both parallel and perpendicular lines?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-328e7d00-6dda-4d62-b6d2-302791c40cf8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes. A figure can have both Parallel and Perpendicular Lines. Some examples are: Letter H, Letter E, Square, Rectangle etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-328e7d00-6dda-4d62-b6d2-302791c40cf8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-328e7d00-6dda-4d62-b6d2-302791c40cf8\"><strong>How many pairs of parallel and perpendicular lines are there in a rectangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-328e7d00-6dda-4d62-b6d2-302791c40cf8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A rectangle has 2 pairs of parallel lines and 4 pairs of perpendicular lines.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Are Parallel and Perpendicular Lines? Parallel and perpendicular lines are two important concepts in geometry. Parallel lines are the lines that never intersect each other. Thus, two parallel lines always maintain a constant distance between them. Perpendicular lines are the two lines that intersect each other at a right angle. We come across examples &#8230; <a title=\"Parallel and Perpendicular Lines &#8211; Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-and-perpendicular-lines\" aria-label=\"More on Parallel and Perpendicular Lines &#8211; Definition With Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1633","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=1633"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1633\/revisions"}],"predecessor-version":[{"id":41424,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1633\/revisions\/41424"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}