Question

For the following figure, state which congruence method can be used to prove the triangle congruent. If no method applies, say none.

Short answer

The triangles are congruent by the $\mathit{S}\mathit{A}\mathit{S}$postulate.

Step-by-step solution

Step 1- Apply the concept of the SAS postulate.

$SAS$ postulates state that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

Step 2- Check the figure.

Consider the figure.

Step 3- Step description.

From the figure, in both the triangles one pair of right angles and two pairs of equal angles.

Using the Isosceles triangle theorem, sides opposite to equal angles are also equal.

So, there are two pairs of equal sides.

Therefore, the triangles are congruent by $SAS$postulates.