{"id":26748,"date":"2023-03-23T10:59:46","date_gmt":"2023-03-23T10:59:46","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26748"},"modified":"2024-01-01T16:40:00","modified_gmt":"2024-01-01T16:40:00","slug":"cpctc-definition-postulates-theorem-proof-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc","title":{"rendered":"CPCTC: Definition, Postulates, Theorem, Proof, 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-bafd5270-ee82-4bea-a960-b32402ae2c4c\" 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\/cpctc#0-what-is-cpctc-in-geometry>What Is CPCTC in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc#3-corresponding-parts>Corresponding Parts<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc#4-cpctc-triangle-congruence>CPCTC Triangle Congruence<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc#8-solved-examples-on-cpctc>Solved Examples on CPCTC<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc#9-practice-problems-on-cpctc>Practice Problems on CPCTC<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc#10-frequently-asked-questions-on-cpctc>Frequently Asked Questions on CPCTC<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-cpctc-in-geometry\">What Is CPCTC in Geometry?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>CPCTC in geometry simply stands for \u201cCorresponding Parts of Congruent Triangles are Congruent.\u201d CPCTC theorem states that if two or more triangles are congruent, then their corresponding angles and sides are congruent as well.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-cpctc-definition\">CPCTC: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">CPCTC meaning is \u201cCorresponding Parts of Congruent Triangles are Congruent.\u201d You can only use CPCTC after you know that two triangles are congruent. What is the CPCTC theorem?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The CPCTC theorem states that if two or more triangles are congruent to each other, then the corresponding angles and the sides of the triangles are also congruent to each other. Let us understand the meaning of congruent triangles and corresponding parts in detail.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-congruent-triangles\">Congruent Triangles<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle has three sides and three angles. The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other. <strong>For two triangles to be congruent, all 3 sides and angles should be congruent<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We also need to remember that when we state that two triangles are congruent, we name them such that the letters for corresponding vertices are in the same order. Take a look at the image given below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"440\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/abc-and-def.png\" alt=\"ABC and DEF\" class=\"wp-image-37151\" title=\"ABC and DEF\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/abc-and-def.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/abc-and-def-300x213.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the figure above, we see that the letters A, B, and C for the vertices of ABC correspond to the letters D, E, and F for the vertices of DEF respectively. We can state the congruences of sides and angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Side congruences: $\\overline{AB} \\cong \\overline{DE},\\; \\overline{BC} &nbsp;\\cong \\overline{EF},\\; \\overline{AC} &nbsp;\\cong \\overline{DF}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Angle congruences: $\\angle ABC \\cong \\angle QRP,\\; &nbsp;\\angle BCA \\cong \\angle RPQ,\\; \\angle CAB \\cong \\angle PQR$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we name the congruent triangles so that the letters for corresponding vertices match up in the triangle congruence statement.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Delta ABC \\cong \\Delta DEF$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-corresponding-parts\">Corresponding Parts<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The corresponding parts of two triangles refer to the parts of two triangles that are in the same relative position<\/strong>. When a triangle\u2019s three sides correspond to those of another triangle, they are at the same location or space. Corresponding angles signify that the three angles of one triangle are located in the same area as those of the other triangle. Take a look at the figure given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"371\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruent-triangles.png\" alt=\"Congruent triangles\" class=\"wp-image-37152\" title=\"Congruent triangles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruent-triangles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruent-triangles-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, $\\Delta MNO \\cong \\Delta XYZ$. It means that the 3 pairs of sides and 3 pairs of angles of $\\Delta MNO$ are congruent to the 3 pairs of corresponding sides and 3 pairs of corresponding angles of $\\Delta XYZ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let&#8217;s identify the 3 corresponding sides and the 3 corresponding angles:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;MN corresponds to XY; NO corresponds to YZ; MO corresponds to XZ.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle M$ corresponds to $\\angle X;\\; \\angle N$ corresponds to $\\angle Y;\\; \\angle O$ corresponds to $\\angle Z$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since $\\Delta MNO \\cong \\Delta XYZ$, as per the CPCTC theorem, the corresponding sides and angles are equal, which means,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$MN = XY,\\; NO = YZ,\\; MO = XZ,$ and<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle M = \\angle X,\\; \\angle N = \\angle Y,\\; \\angle O = \\angle Z$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-cpctc-triangle-congruence\">CPCTC Triangle Congruence<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the CPCTC, all of the corresponding sides and angles are congruent when two triangles are congruent by any criteria. Here, we&#8217;ll talk about five triangle congruence criteria or postulates.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"996\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/cpctc-triangle-congruence.png\" alt=\"CPCTC triangle congruence\" class=\"wp-image-37154\" title=\"CPCTC triangle congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/cpctc-triangle-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/cpctc-triangle-congruence-187x300.png 187w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Visually, we can represent the rules as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"701\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/rules-for-triangle-congruence.png\" alt=\"Rules for triangle congruence\" class=\"wp-image-37155\" title=\"Rules for triangle congruence\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/rules-for-triangle-congruence.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/rules-for-triangle-congruence-265x300.png 265w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-cpctc-proof\">CPCTC Proof<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Once it is shown that two triangles are congruent using one of the above congruence methods, we also know that all corresponding parts of the congruent triangles are congruent (abbreviated CPCTC).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let&#8217;s consider an example:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-cpctc.png\" alt=\"Proof of CPCTC\" class=\"wp-image-37156\" title=\"Proof of CPCTC\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-cpctc.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/proof-of-cpctc-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider $\\Delta DAB$ and $\\Delta DCB$ in which $BA = BC$ and $AD = DC$ are given.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let&#8217;s prove the CPCTC theorem.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$BA = BC$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$AD = DC$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$BD = BD$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Reflexive Property)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $Delta DAB \\cong DCB$ by SSS criteria (Side-Side-Side)&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the two triangles are congruent, we can use the CPCTC property and write<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle DAB&nbsp; \\cong&nbsp; \\angle DCB,\\; \\angle ADB \\cong \\angle CDB$ and&nbsp; $\\angle ABD \\cong&nbsp; \\angle CBD$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">There are five conditions to determine if two triangles are congruent. They are<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;SSS, AAS, SAS, ASA, and HL criteria.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">SSS, AAS, SAS, ASA, HL use corresponding parts to prove triangles congruent, while CPCTC uses congruent triangles to prove corresponding parts congruent.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">By CPCTC, if two triangles are congruent, then you know that all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">&nbsp;We use the symbol $\u201c\\cong\u201d$ to denote congruence.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If you know the two triangles are congruent, you need to match up the letters for their corresponding vertices, and then use those to state the congruences of angles and sides.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned in detail about the CPCTC definition, theorem, and proof. Let\u2019s solve some examples and practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples-on-cpctc\">Solved Examples on CPCTC<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1: Given <\/strong>$\\overline{YX} \\cong \\overline{YZ},\\; \\angle XYW \\cong \\angle ZYW$<strong>, prove that <\/strong>$\\overline{XW}&nbsp; \\cong&nbsp; \\overline{ZW}$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"200\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruence-in-wxy-and-wzy.png\" alt=\"Congruence in WXY and WZY\" class=\"wp-image-37157\" title=\"Congruence in WXY and WZY\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruence-in-wxy-and-wzy.png 308w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/congruence-in-wxy-and-wzy-300x195.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$YX \\cong YZ$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle XYW \\cong \\angle ZYW$ &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$WY \\cong WY$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Reflexive property)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\Delta WXY \\cong \\Delta WZY$&nbsp; by SAS criteria (Side-Angle-Side)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $XW \\cong ZW$&nbsp; (by CPCTC)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2:<\/strong> <strong>Given: <\/strong>$\\angle A \\cong \\angle C$<strong>, BY bisects <\/strong>$\\angle ABC$<strong>. Prove that <\/strong>$\\overline{AB}&nbsp;\\cong \\overline{CB}$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"231\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/Congruence-in-adb-and-cdb.png\" alt=\"Congruence in ADB and CDB\" class=\"wp-image-37158\" title=\"Congruence in ADB and CDB\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$\\angle A \\cong \\angle C$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;BY bisects $\\angle ABC$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ABY \\cong \\angle CBY$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Definition of angle Bisector)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$BY&nbsp; \\cong&nbsp; BY$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Reflexive property\/common side)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Delta AYB \\cong \\Delta CYB$&nbsp; by AAS criteria&nbsp; (Angle-Angle-Side)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus,&nbsp; $\\overline{AB}&nbsp; \\cong&nbsp;\\overline{CB}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (CPCTC)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 3:<\/strong> <strong>Observe the figure given below and find the measure of <\/strong>$\\angle I$<strong>&nbsp; and length of <\/strong>$\\overline{VU}$<strong>&nbsp; using the CPCTC theorem, if <\/strong>$\\Delta HJI \\cong \\Delta TVU$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"599\" height=\"147\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-and-congruence-of-corresponding-sides-and-angles.png\" alt=\"Measures and congruence of corresponding sides and angles\" class=\"wp-image-37159\" title=\"Measures and congruence of corresponding sides and angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-and-congruence-of-corresponding-sides-and-angles.png 599w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-and-congruence-of-corresponding-sides-and-angles-300x74.png 300w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Given that $\\Delta HJI \\cong \\Delta TVU$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By applying the CPCTC theorem,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\overline{HJ} = \\overline{TV} = 25\\; mm$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\angle HJI \\cong \\angle VTU$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\overline{HI}&nbsp; \\cong&nbsp;\\overline{TU} = 50\\; mm$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can identify that $\\overline{JI}$ and $\\overline{VU}$ are the corresponding sides of two congruent triangles $\\Delta HJI$ and $\\Delta TVU$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $\\overline{JI} = \\overline{VU} = 43$ units&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the length of $\\overline{VU}$&nbsp; is 43 units.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, by the same theorem,&nbsp; $\\angle I = \\angle U$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\angle I = 30^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 4: Observe the figure given below, in which <\/strong>$AC = CD$<strong> and BC is perpendicular to AD. Find y by using the CPCTC theorem<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"259\" height=\"229\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measure-and-congruence-of-corresponding-sides-and-an-angle.png\" alt=\"Measure and congruence of corresponding sides and an angle\" class=\"wp-image-37160\" title=\"Measure and congruence of corresponding sides and an angle\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>First let us prove that $\\Delta ABC \\cong \\Delta BCD$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AC = CD$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$BC = BC$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (common side)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle BCA = \\angle BCD$ (as BC is perpendicular to AD)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\Delta ABC \\cong \\Delta BCD$ (SAS criterion)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AB = BD$ ( By CPCTC)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now as $AB = BD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $6y = 48$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = 8$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 5: Observe the figure given below in which <\/strong>$\\angle PQR = \\angle STU$ and $\\angle PRQ&nbsp; = \\angle SUT$<strong>, <\/strong>$\\overline{QR} = \\overline{TU}$<strong>. Find the value of x and y by using the CPCTC theorem.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"564\" height=\"137\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-of-corresponding-angles-and-a-side.png\" alt=\"Measures of corresponding angles and a side\" class=\"wp-image-37162\" title=\"Measures of corresponding angles and a side\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-of-corresponding-angles-and-a-side.png 564w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/measures-of-corresponding-angles-and-a-side-300x73.png 300w\" sizes=\"auto, (max-width: 564px) 100vw, 564px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> $\\angle PQR = \\angle STU$ &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\angle PRQ&nbsp; = \\angle SUT$&nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\overline{QR} = \\overline{TU}$ &nbsp; &nbsp; &nbsp; (Given)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\Delta RPQ \\cong&nbsp; \\Delta UST$&nbsp; (ASA criterion)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As $\\angle R = \\angle U$, we get $x = 30^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The value of $x = 30^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As we know, sum of three angles $= 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle R + \\angle P + \\angle Q&nbsp; = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$30^{\\circ} + \\angle P + 60^{\\circ} =&nbsp; 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\angle P = 180 \\;-\\; 90 = 90^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, by CPCTC, we know $\\angle P = \\angle S$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\angle S = y = 90^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The value of $y =&nbsp; 90^{\\circ}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems-on-cpctc\">Practice Problems on CPCTC<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">CPCTC: Definition, Postulates, Theorem, Proof, 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\">What does CPCTC in math stand for?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Common parts of congruent triangles are congruent.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Corresponding parts of congruent triangles are congruent.<\/div><div class=\"spq_answer_block\" data-value=\"2\">Corresponding parts of corresponding triangles are corresponding.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Corresponding parts of Triangles are congruent.<\/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: Corresponding parts of congruent triangles are congruent.<br\/>CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.<\/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\">If two triangles are congruent,it  means that all of its corresponding _________ and _________ are congruent.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">angles, triangles<\/div><div class=\"spq_answer_block\" data-value=\"1\">points, angles<\/div><div class=\"spq_answer_block\" data-value=\"2\">sides, angles<\/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: sides, angles<br\/>If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">CPCTC theorem is used only when two triangles are ___.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">congruent<\/div><div class=\"spq_answer_block\" data-value=\"1\">similar<\/div><div class=\"spq_answer_block\" data-value=\"2\">right triangles<\/div><div class=\"spq_answer_block\" data-value=\"3\">not congruent<\/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: congruent<br\/>CPCTC is used only when two triangles are congruent. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which criteria proves these two triangles congruent?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-4-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">SSS<\/div><div class=\"spq_answer_block\" data-value=\"1\">SAS<\/div><div class=\"spq_answer_block\" data-value=\"2\">HL<\/div><div class=\"spq_answer_block\" data-value=\"3\">ASA<\/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: ASA<br\/>ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What additional information is required for the 2 triangles to be congruent by ASA?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-5.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\overline{IJ}  \\cong  \\overline{UV}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\angle J  \\cong \\angle V$ or $\\angle K \\cong  \\angle W$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\angle J  \\cong \\angle V$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\overline{JK}  \\cong \\overline{VW}$<\/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: $\\overline{IJ}  \\cong  \\overline{UV}$<br\/>ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.<\/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\": \"CPCTC: Definition, Postulates, Theorem, Proof, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"CPCTC\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What does CPCTC in math stand for?\",\n                    \"text\": \"What does CPCTC in math stand for?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Common parts of congruent triangles are congruent.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Corresponding parts of corresponding triangles are corresponding.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Corresponding parts of Triangles are congruent.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Corresponding parts of congruent triangles are congruent.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"CPCTC stands for Corresponding Parts of Congruent Triangles are \r\nCongruent.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If two triangles are congruent,it  means that all of its corresponding _________ and _________ are congruent.\",\n                    \"text\": \"If two triangles are congruent,it  means that all of its corresponding _________ and _________ are congruent.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"angles, triangles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"points, angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\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 triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"sides, angles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If two triangles are congruent, then all pairs of corresponding sides are congruent and all pairs of corresponding angles are congruent.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"CPCTC theorem is used only when two triangles are ___.\",\n                    \"text\": \"CPCTC theorem is used only when two triangles are ___.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"similar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"right triangles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"not congruent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"congruent\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"CPCTC is used only when two triangles are congruent. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which criteria proves these two triangles congruent?\",\n                    \"text\": \"Which criteria proves these two triangles congruent? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-4-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"SSS\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"SAS\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"HL\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"ASA\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"ASA is angle-side-angle. Given that, two corresponding angles and the included side are equal, the remaining corresponding angles and the other 2 corresponding sides are also equal by CPCTC.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What additional information is required for the 2 triangles to be congruent by ASA?\",\n                    \"text\": \"What additional information is required for the 2 triangles to be congruent by ASA? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-5.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle J  \\\\cong \\\\angle V$$ or $$\\\\angle K \\\\cong  \\\\angle W$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle J  \\\\cong \\\\angle V$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\overline{JK}  \\\\cong \\\\overline{VW}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\overline{IJ}  \\\\cong  \\\\overline{UV}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"ASA is angle-side-angle.If any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions-on-cpctc\">Frequently Asked Questions on CPCTC<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-13141a29-0735-400b-b6f7-eec36fe5e3ce\" 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-0-13141a29-0735-400b-b6f7-eec36fe5e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-13141a29-0735-400b-b6f7-eec36fe5e3ce\"><strong>What is reflexive property?<\/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-0-13141a29-0735-400b-b6f7-eec36fe5e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The reflexive property states that any line segment or angle or shape is congruent to itself.<\/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-1-13141a29-0735-400b-b6f7-eec36fe5e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-13141a29-0735-400b-b6f7-eec36fe5e3ce\"><strong>What must be proven before using CPCTC?<\/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-1-13141a29-0735-400b-b6f7-eec36fe5e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To prove CPCTC, we first prove the triangles congruent using SSS, AAS, SAS, ASA, or HL. Next, we can use CPCTC, which states that the other parts of the triangle are also congruent.<\/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-2-13141a29-0735-400b-b6f7-eec36fe5e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-13141a29-0735-400b-b6f7-eec36fe5e3ce\"><strong>When and why is CPCTC used?<\/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-2-13141a29-0735-400b-b6f7-eec36fe5e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">CPCTC is commonly used at or near the end of a proof, which asks the student to show that the two sides or angles are congruent. It is frequently used to assess the similarity and congruence of two or more triangles.<\/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-3-13141a29-0735-400b-b6f7-eec36fe5e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-13141a29-0735-400b-b6f7-eec36fe5e3ce\"><strong>What is the third angle theorem?<\/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-3-13141a29-0735-400b-b6f7-eec36fe5e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also be congruent. This is called the third angle theorem.<\/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-4-13141a29-0735-400b-b6f7-eec36fe5e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-13141a29-0735-400b-b6f7-eec36fe5e3ce\"><strong>Is CPCTC true for similar triangles?<\/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-4-13141a29-0735-400b-b6f7-eec36fe5e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In similar triangles, corresponding angles are equal, whereas corresponding sides of the triangles are not equal but proportional. So, we cannot apply the CPCTC theorem for similar triangles.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is CPCTC in Geometry? CPCTC in geometry simply stands for \u201cCorresponding Parts of Congruent Triangles are Congruent.\u201d CPCTC theorem states that if two or more triangles are congruent, then their corresponding angles and sides are congruent as well. CPCTC: Definition CPCTC meaning is \u201cCorresponding Parts of Congruent Triangles are Congruent.\u201d You can only use &#8230; <a title=\"CPCTC: Definition, Postulates, Theorem, Proof, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/cpctc\" aria-label=\"More on CPCTC: Definition, Postulates, Theorem, Proof, 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-26748","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\/26748","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=26748"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26748\/revisions"}],"predecessor-version":[{"id":37163,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26748\/revisions\/37163"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}