![]() Corresponding angles of the two similar triangles are equal, whereas, corresponding sides of the triangles are not equal, but proportional. So, we cannot apply the CPCTC theorem for similar triangles. What is CPCTC for Similar Triangles?ĬPCTC for similar triangles is not true. Corresponding means angles and sides that are in the same respective position in the two triangles. CPCTC is a theorem that says corresponding parts of congruent triangles are congruent. AB = LM, BC = MN, AC = LN, and ∠ A = ∠L, ∠B = ∠M, ∠C = ∠N. And if △ABC ≅ △LMN, then as per the CPCTC theorem, the corresponding sides and angles are equal, i.e. ∠A corresponds to ∠L, ∠B corresponds to ∠M, ∠C corresponds to ∠N. AB corresponds to LM, BC corresponds to MN, AC corresponds to LN. the three corresponding sides and the three corresponding angles. In these two triangles ABC and LMN, let us identify the 6 parts: i.e. ![]() It means that the three pairs of sides and three pairs of angles of △ABC are equal to the three pairs of corresponding sides and three pairs of corresponding angles of △LMN. Corresponding angles mean the three angles in one triangle are in the same position or spot as in the other triangle. ![]() Two congruent triangles have three equal sides and equal angles with respect to each other.Ĭorresponding sides mean the three sides in one triangle are in the same position or spot as in the other triangle. Two triangles are said to be congruent if they have exactly the same size and the same shape. Let us understand the meaning of congruent triangles and corresponding parts in detail. This means, when two or more triangles are congruent then their corresponding sides and angles are also congruent or equal in measurements. The CPCTC theorem states that when two triangles are congruent, then every corresponding part of one triangle is congruent to the other. To offer financial support, visit my Patreon page.The abbreviation CPCTC is for Corresponding Parts of Congruent Triangles are Congruent. We are open to collaborations of all types, please contact Andy at for all enquiries. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. Andymath content has a unique approach to presenting mathematics. Visit me on Youtube, Tiktok, Instagram and Facebook. In the future, I hope to add Physics and Linear Algebra content. Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. If you have any requests for additional content, please contact Andy at He will promptly add the content. About Ī is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. These theorems prove the congruence of triangles and are often used in the step prior to CPCTC. Therefore proofs using CPCTC usually also contain at least one of the following theorems, SSS, SAS, ASA, AAS, or HL. Using CPCTC in proofs is typically covered in a high school geometry class.ĬPCTC will only work if 2 triangles are know to be congruent. Once we know that two triangles are congruent, we can conclude that any previously unknown corresponding parts must also be congruent. In Summary Proving triangle congruence using CPCTC, or “corresponding parts of congruent triangles are congruent” theorem, is a key concept in geometry.
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