Congruent Triangle

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Congruent triangles are the triangles which have their respective corresponding sides and corresponding angles equal to each other. This implies that the corresponding sides of one triangle are equal to the corresponding sides of the other triangle. Similarly, corresponding angles of one triangle are equal to the corresponding angles of the other triangle, and then the two triangles are called as congruent triangles. Congruency between two triangles can be proved using congruency properties such as SAS, SSS, ASA, AAS and HL (only for right triangles).

Example 1: In triangle ABC, angle ABC is 35º, angle ACB is 75º and side BC = 5m. In triangle XYZ, angle XYZ is 35º, angle XZY is 75º and side YZ is 5m. Are ABC and XYZ congruent triangles?



According to ASA (Angle-included side-Angle congruency property), corresponding 2 angles and an included side are equal in both the triangles and hence they are congruent triangles.


Example 2: In triangle ABC, side AB = 3m, side AC = 4m and angle BAC is 62º. In triangle PQR, side PQ = 3m, PR= 4m and a
ngle QPR is 62º. Are ABC and PQR congruent triangles?



According to SAS (Side-included Angle-Side congruency property), corresponding 2 sides and an included angle are equal in both the triangles and hence they are congruent triangles.

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