{"id":25674,"date":"2023-03-01T14:32:22","date_gmt":"2023-03-01T14:32:22","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=25674"},"modified":"2024-01-10T16:40:41","modified_gmt":"2024-01-10T16:40:41","slug":"bisect-definition-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/bisect","title":{"rendered":"Bisect: Definition, Formula, Examples"},"content":{"rendered":"<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-3fb7c4cb-772c-4dc6-a935-03fa79a515a9\" 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\/bisect#0-what-is-a-bisect>What is a Bisect?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/bisect#3-bisecting-an-angle-steps-of-construction>Bisecting an Angle: Steps of Construction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/bisect#4-bisecting-a-shape>Bisecting a Shape<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/bisect#7-solved-examples-on-bisect>Solved Examples on Bisect<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/bisect#8-practice-problems-on-bisect>Practice Problems on Bisect<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/bisect#9-frequently-asked-questions-on-bisect>Frequently Asked Questions on Bisect<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-bisect\">What is a Bisect?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To bisect in geometry simply means <strong>dividing a shape into two equal parts<\/strong>. In life, we come across many situations, where we need to divide something equally among two parts. When an object is divided into two identical parts, each part is called a \u201chalf,\u201d denoted as a fraction $\\frac{1}{2}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, when we divide a pizza into two equal parts, it is called \u201cbisection.\u201d<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisect-example-with-a-pizza\u200b\u200b.png\" alt=\"Bisect example with a pizza\u200b\u200b\" class=\"wp-image-37298\" title=\"Bisect example with a pizza\u200b\u200b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisect-example-with-a-pizza\u200b\u200b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisect-example-with-a-pizza\u200b\u200b-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-bisect-definition\">Bisect: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To understand the word bisect, we need to ask a question, what does bisect mean? The definition of \u201cbisect\u201d can be given as a mathematical process of dividing a geometrical figure into two parts of equal sizes.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can bisect various objects, such as lines, angles, and other closed shapes. The term <strong>bisect<\/strong> in geometry is usually used when a line segment or an angle is divided into two equal parts.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, bisection of a line segment is defined as dividing the line segment into two line segments of equal lengths. Bisecting a closed shape means dividing it in two shapes of equal area.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u201cBisect\u201d examples:<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Bisecting an angle<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"308\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-an-angle.png\" alt=\"Bisecting an angle\" class=\"wp-image-37299\" title=\"Bisecting an angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-an-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-an-angle-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Bisecting a segment<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-segment.png\" alt=\"Bisecting a segment\" class=\"wp-image-37301\" title=\"Bisecting a segment\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-segment.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-segment-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-bisecting-a-line-segment-steps-of-construction\">Bisecting a Line Segment: Steps of Construction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To bisect a line segment, we create circular arcs, on either side of the line segment, from both ends of the line segment, where these circular arcs meet on either side and are then marked and connected, intersecting the original line segment at a point that bisects it. Let\u2019s understand it better with the proper steps of construction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1: <\/strong>Draw the line segment of the given length, say AB.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2:<\/strong> Open a compass to the distance equal to roughly more than half of the length of AB.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3: <\/strong>Cut two arcs on either side of the line segment AB, centered on A.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 4: <\/strong>Repeat step 3 but from B, make sure to keep the radius of the arcs the same as in step 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/drawing-arcs-to-bisect-a-line-segment.png\" alt=\"Drawing arcs to bisect a line segment\" class=\"wp-image-37302\" title=\"Drawing arcs to bisect a line segment\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/drawing-arcs-to-bisect-a-line-segment.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/drawing-arcs-to-bisect-a-line-segment-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 5: <\/strong>Mark the points where the arcs meet on either side of the line segment, say P and Q respectively.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 6:<\/strong> Join PQ, and mark the point where PQ intersects AB as C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-for-bisecting-a-line-segment.png\" alt=\"Steps for bisecting a line segment\" class=\"wp-image-37303\" title=\"Steps for bisecting a line segment\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-for-bisecting-a-line-segment.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-for-bisecting-a-line-segment-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 7:<\/strong> AC and BC are bisections of the line segment AB.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-line-segment-construction.png\" alt=\"Bisecting a line segment: construction\" class=\"wp-image-37304\" title=\"Bisecting a line segment: construction\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-line-segment-construction.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-line-segment-construction-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Note: The bisector formed here is a perpendicular bisector.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-bisecting-an-angle-steps-of-construction\">Bisecting an Angle: Steps of Construction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To bisect an angle means to draw a ray originating from the vertex of the angle in such a way that the angles formed on either side of this ray are equal to each other and half of the original angle. To achieve this, we draw an arc of arbitrary radius centered at the vertex of the angle, such that the arc bisects both the arms of the angle and then we mark these points. Now we draw two more arcs from these new points such that they intersect in front of the angle and we once again mark this intersection, and finally, if we join this point to the vertex of the angle, we have successfully bisected the angle. Let\u2019s understand it better with the proper steps of construction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1: <\/strong>Draw the given angle with the help of a protractor, say $\\angle AOB$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2: <\/strong>Open a compass to a small radius, and cut an arc centered at O such that it intersects both arms of $\\angle AOB$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3:<\/strong> Mark the intersections at both arms X and Y respectively.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 4: <\/strong>Cut two more arcs in front of $\\angle AOB$ centered at X and Y each.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Mark the point where the arcs intersect as C.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Draw a ray originating at O passing through C.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle AOC$ and $\\angle BOC$ are the required bisections of $\\angle AOB$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The following image shows the steps for the construction of an angle bisector followed by a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"364\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-1-and-2-of-constructing-an-angle-bisector.png\" alt=\"Steps 1 and 2 of constructing an angle bisector\" class=\"wp-image-37305\" title=\"Steps 1 and 2 of constructing an angle bisector\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-1-and-2-of-constructing-an-angle-bisector.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-1-and-2-of-constructing-an-angle-bisector-300x176.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"398\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-3-and-4-of-constructing-an-angle-bisector.png\" alt=\"Steps 3 and 4 of constructing an angle bisector\" class=\"wp-image-37306\" title=\"Steps 3 and 4 of constructing an angle bisector\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-3-and-4-of-constructing-an-angle-bisector.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/steps-3-and-4-of-constructing-an-angle-bisector-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-bisecting-a-shape\">Bisecting a Shape<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To bisect a shape, we need to divide the shape into two parts of equal area. For symmetric shapes, we can draw a line that divides the shape into two identical halves. Take a look at the following figure!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"352\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-triangle-square-and-a-circle.png\" alt=\"Bisecting a triangle, square, and a circle\" class=\"wp-image-37307\" title=\"Bisecting a triangle, square, and a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-triangle-square-and-a-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-triangle-square-and-a-circle-300x170.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To bisect a symmetrical shape, we can simply cut it along a line of symmetry and the shape will be bisected into two shapes of equal area. These are known as trivial bisectors of symmetric shapes.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are also some shapes that can be bisected by different lines other than lines of symmetry. These other lines are usually their medians.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Bisect means to divide into two equal parts.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">We can mark any point on a line and it\u2019ll be a bisector since a line can be extended infinitely long on either side. Hence, a line has infinite bisectors.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A circle also has an infinite number of bisectors since it has an infinite number of lines of symmetry along each of its diameters.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the concept of bisection in geometry. Bisection means dividing a geometrical object into two equal parts. The equality of the two parts is defined differently for different objects, for line segments and curves it is defined as dividing it into two equal lengths, for angles its two equal angles, and for closed shapes, it&#8217;s two shapes of equal areas. We also learned the steps of construction for bisecting line segments and angles.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-bisect\">Solved Examples on Bisect<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the following image if the m<\/strong>$\\angle ABC = 80^{\\circ}$<strong>. BD is an angle bisector of <\/strong>$\\angle ABC$<strong>. BE is an angle bisector of angle ABD, then find the measure of angle ABE?<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"329\" height=\"321\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/applying-properties-of-an-angle-bisector.png\" alt=\"Applying properties of an angle bisector\" class=\"wp-image-37308\" title=\"Applying properties of an angle bisector\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/applying-properties-of-an-angle-bisector.png 329w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/applying-properties-of-an-angle-bisector-300x293.png 300w\" sizes=\"auto, (max-width: 329px) 100vw, 329px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>The angle bisector divides the angle into half.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">BD is angle bisector of angle ABC.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle ABD = \\frac{1}{2}m\\angle ABC$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m\\angle ABD = \\frac{1}{2} \\times 80 = 40^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, since BE is angle bisector of angle ABD, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle ABE = \\frac{1}{2} mABD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m\\angle ABE = \\frac{1}{2} \\times 40$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow m\\angle ABE = 20^{\\circ}$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>What is the value of x in the following image, if M is the midpoint of PQ?<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"461\" height=\"91\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-length-using-property-of-segment-bisector.png\" alt=\"Finding the missing length using property of segment bisector\" class=\"wp-image-37309\" title=\"Finding the missing length using property of segment bisector\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-length-using-property-of-segment-bisector.png 461w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-the-missing-length-using-property-of-segment-bisector-300x59.png 300w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">M is the midpoint of PQ.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$PM = MQ = \\frac{1}{2} PQ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= \\frac{1}{2} \\times 24$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$= 12$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, x $=$ MQ $= 12$ inches<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>A farmer has farmland of the isosceles trapezoid shape. He divides it equally between his two children. How much farmland will each child get?<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>[ Use: Area of trapezoid <\/strong>$= \\frac{1}{2} \\times (Sum\\; of\\; the\\; parallel\\; sides) \\times Height$ <strong>]<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/an-isosceles-trapezoid-with-legs-20-yds-and-parallel-sides-8-yds-20-yds.png\" alt=\"An isosceles trapezoid with legs 20 yds and parallel sides 8 yds &amp; 20 yds\" class=\"wp-image-37310\" title=\"An isosceles trapezoid with legs 20 yds and parallel sides 8 yds &amp; 20 yds\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/an-isosceles-trapezoid-with-legs-20-yds-and-parallel-sides-8-yds-20-yds.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/an-isosceles-trapezoid-with-legs-20-yds-and-parallel-sides-8-yds-20-yds-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/an-isosceles-trapezoid-with-legs-20-yds-and-parallel-sides-8-yds-20-yds-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/an-isosceles-trapezoid-with-legs-20-yds-and-parallel-sides-8-yds-20-yds-120x120.png 120w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the image, we can see that the farmland is in the shape of an isosceles trapezium. The bisection can be done by drawing a bisector through the mid-points of the parallel sides since an isosceles trapezium is symmetrical along this line.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-trapezoid-shape.png\" alt=\"Bisecting a trapezoid shape\" class=\"wp-image-37311\" title=\"Bisecting a trapezoid shape\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-trapezoid-shape.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-trapezoid-shape-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-trapezoid-shape-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/bisecting-a-trapezoid-shape-120x120.png 120w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area of the entire farmland $= \\frac{1}{2} \\times (Sum\\; of\\; the\\; parallel\\; sides) \\times Height$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, substituting the width of the farmland for the height of the trapezium, we have,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Area Area $= \\frac{1}{2} \\times (20 + 8) \\times 20 = \\frac{1}{2} \\times 28 \\times 20 =280\\; yards^{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The area of the farmland is 280 sq. yards.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">After bisection, both children will get 140 sq. yards of the farmland.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-bisect\">Practice Problems on Bisect<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Bisect: Definition, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">A point on a line segment equidistant from the endpoints of the same is called a __________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">center<\/div><div class=\"spq_answer_block\" data-value=\"1\">midpoint<\/div><div class=\"spq_answer_block\" data-value=\"2\">incenter<\/div><div class=\"spq_answer_block\" data-value=\"3\">centroid<\/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: midpoint<br\/>A point at the exact middle of the line segment is the midpoint of the line segment.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">How many trivial bisectors does a square have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">1<\/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: 4<br\/>A square has 4 lines of symmetry. It has 4 trivial bisectors.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the measure of angle ABC, given that BD is the angle bisector.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/bisect-practice-problem.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$110^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$120^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$130^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$150^{\\circ}$<\/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: $130^{\\circ}$<br\/>Angle bisectors divide the angle in two halves. The angle ABD is half of angle ABC, which means angle ABC is double of ABD. Thus, $m\\angle ABC = 2 \\times 65^{\\circ} = 130^{\\circ}$<\/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\": \"Bisect: Definition, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Bisect\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A point on a line segment equidistant from the endpoints of the same is called a __________.\",\n                    \"text\": \"A point on a line segment equidistant from the endpoints of the same is called a __________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"center\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"incenter\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"centroid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"midpoint\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A point at the exact middle of the line segment is the midpoint of the line segment.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many trivial bisectors does a square have?\",\n                    \"text\": \"How many trivial bisectors does a square have?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A square has 4 lines of symmetry. 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Thus, $$m\\\\angle ABC = 2 \\\\times 65^{\\\\circ} = 130^{\\\\circ}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-bisect\">Frequently Asked Questions on Bisect<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\" 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-0-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\"><strong>What is a perpendicular bisector?<\/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-0-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A perpendicular bisector is a line segment that is perpendicular to another line segment and also passes through the midpoint of the same.<\/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-1-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\"><strong>Can a point be bisected?<\/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-1-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A point has no dimensions, therefore, there is nothing to be divided into two equal parts in a point. Thus a point cannot be bisected.<\/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-2-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\"><strong>Why is bisection important?<\/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-2-9e97d7ac-9a8e-4c00-928c-b82faa7a311b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Bisection is an important part of geometry; many shapes and geometrical objects are drawn with the help of bisection, and we know that geometrical knowledge is important in architecture and some branches of engineering.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is a Bisect? To bisect in geometry simply means dividing a shape into two equal parts. In life, we come across many situations, where we need to divide something equally among two parts. When an object is divided into two identical parts, each part is called a \u201chalf,\u201d denoted as a fraction $\\frac{1}{2}$.&nbsp; For &#8230; <a title=\"Bisect: Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/bisect\" aria-label=\"More on Bisect: Definition, Formula, 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-25674","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\/25674","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=25674"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25674\/revisions"}],"predecessor-version":[{"id":37312,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/25674\/revisions\/37312"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=25674"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=25674"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=25674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}