Congruent Triangles: SSS, SAS, ASA

Congruent Triangles: SSS, SAS, ASA

Read each question carefully and determine if the given triangles are congruent. If they are, state the postulate (SSS, SAS, or ASA) that proves congruence. If not, write 'Not congruent'.

1. Which postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent?

2. In the triangles below, AB = DE, BC = EF, and ∠B = ∠E. Which postulate proves that △ABC ≅ △DEF?

3. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent by the   postulate.

4. The   postulate requires two sides and the included angle to be congruent for two triangles to be congruent.

5. Consider two triangles, △XYZ and △PQR. If XY = PQ, YZ = QR, and XZ = PR, are the triangles congruent? If so, by which postulate? Explain your reasoning.

6. Draw two triangles that are congruent by the ASA postulate. Label the vertices and mark the congruent parts.

7. The Angle-Side-Side (ASS) postulate is a valid method to prove triangle congruence.

8. If two triangles have corresponding angles that are congruent, then the triangles must be congruent.

Match each congruence postulate with its description.