The theorem CPCTC tells that when two triangles are congruent then their corresponding sides and angles are also said to be congruent. Sometimes, it is also called CPCT which means corresponding parts of congruent triangles. What does CPCTC Stand for?ĬPCTC stands for corresponding parts of congruent triangles are congruent. It can be justified by superimposing triangles on each other and then by observing the corresponding angles and side lengths. How do you Prove CPCTC?Īfter showing the proposed triangles are congruent, we can immediately say that the corresponding parts of congruent triangles are congruent. 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. Prove that ∠DEF ≅ ∠GHI.The abbreviation CPCTC is for Corresponding Parts of Congruent Triangles are Congruent. A and B are the endpoints of a bridge going over a river.How do we use CPCTC to prove corresponding parts of triangles?ĬPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and is used to justify two triangles are congruent in a proof. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.ĬPCTC is an acronym for corresponding parts of congruent triangles are congruent. Videos, worksheets, solutions, and activities to help Geometry students learn about CPCTC.
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