Congruent Triangles Examples
Postulates and theorems on congruent triangles are discussed using examples. More congruent triangles problems with detailed solutions are presented.
Side-Angle-Side (SAS) Congruence PostulateIf 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.Example 1Let ABCD be a parallelogram and AC be one of its diagonals. What can you say about triangles ABC and CDA? Explain your answer.Solution to Example 1
Side-Side-Side (SSS) Congruence PostulateIf 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.Example 2Let ABCD be a square and AC be one of its diagonals. What can you say about triangles ABC and CDA? Explain your answer.Solution to Example 2
Angle-Side-Angle (ASA) Congruence PostulateIf two angles (ACB, ABC) and the included side (BC) of a triangle are congruent to the corresponding two angles (A'C'B', A'B'C') and included side (B'C') in another triangle, then the two triangles are congruent.Example 3ABC is an isosceles triangle. BB' is the angle bisector. Show that triangles ABB' and CBB' are congruent.Solution to Example 3
Angle-Angle-Side (AAS) Congruence TheoremIf two angles (BAC, ACB) and a side opposite one of these two angles (AB) of a triangle are congruent to the corresponding two angles (B'A'C', A'C'B') and side (A'B') in another triangle, then the two triangles are congruent.Example 4Solution to Example 4
Right Triangle Congruence TheoremIf the hypotenuse (BC) and a leg (BA) of a right triangle are congruent to the corresponding hypotenuse (B'C') and leg (B'A') in another right triangle, then the two triangles are congruent.Example 5Show that the two right triangles shown below are congruent.Solution to Example 5
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