Question

1. look at the figures. how can you prove the triangles are congruent?

△abc=△def by the sas postulate.
it is not possible to determine if the triangles are congruent.
△abc=△def by the sss postulate.

Explanation:

Step1: Recall congruent triangle postulates

The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. The SSS (Side - Side - Side) postulate states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Step2: Analyze the given triangles

In \(\triangle ABC\) and \(\triangle DEF\), we have two pairs of sides marked as equal (from the tick - marks). But we are not given information about the third pair of sides. Also, the right angles (\(\angle A=\angle D = 90^{\circ}\)) are not the included angles for the given pairs of sides.

Answer:

It is not possible to determine if the triangles are congruent.