Question

are these shapes congruent?

Explanation:

Step1: Check side lengths

In the first shape, sides are 22 in and 16 in. In the second shape, sides are 16 in and 22 in. So side lengths match.

Step2: Check angle measures

First shape has angles \(42^{\circ},138^{\circ},138^{\circ},42^{\circ}\). Second shape has angles \(42^{\circ},138^{\circ},138^{\circ},42^{\circ}\). Angle measures match.

Step3: Congruence criteria

Since all corresponding sides and angles are equal, by the definition of congruent polygons (all corresponding sides and angles are congruent), the shapes are congruent.

Answer:

yes