Question

These triangles are congruent by the triangle congruence postulate [?]

Answer 1

Given:

A figure of two congruent triangles.

To find:

The triangle congruence postulate by which the given triangles are congruent.

Solution:

First label the vertices as shown below.

In triangle ABC and triangle CDA,

$AB\cong CD$                   (Given)

$\angle BAC\cong \angle DCA$                   (Given)

$AC\cong AC$                  (Common side)

The corresponding two sides and their included angle are congruent in both triangles. So, triangles are congruent by SAS congruence postulate.

$\Delta ABC\cong \Delta CDA$            [SAS congruence postulate]

Therefore, the correct option is B.