The two triangles also have a common side: AC.Hence sidesĪB and CD are congruent, and also sides BC and DA are congruent. In a square, all four sides are congruent.What can you say about triangles ABC and CDA? Explain your answer. Let ABCD be a square and AC be one of its diagonals. If the three sides ( AB, BC and CA ) of a triangle are congruent to the corresponding three sides ( A'B', B'C' and C'A' ) in another triangle, then the two triangles are congruent. Side-Side-Side (SSS) Congruence Postulate According to the above postulate the two triangles ABC and CDA are congruent. Two sides and an included angle of triangle ABC are congruent to two corresponding sides and an included angle in triangle CDA.In a parallelogram opposite angles are congruent.Hence sidesīC and AD are congruent, and also sides AB and CD are congruent. In a parallelogram, opposite sides are congruent.Let ABCD be a parallelogram and AC be one of its diagonals. If two sides ( CA and CB ) and the included angle ( BCA ) of a triangle are congruent to the corresponding two sides ( C'A' and C'B' ) and the included angle ( B'C'A' ) in another triangle, then the two triangles are congruent. Side-Angle-Side (SAS) Congruence Postulate More problems on congruent triangles with detailed solutions are included. Postulates and theorems on congruent triangles are discussed using examples. Congruent Triangles Problems with Solutions
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