Exercise 42 Page 502

To find whether the parallelograms are congruent, let's begin by recalling that the figures are congruent if they satisfy two conditions.

1. They have congruent corresponding angles.
2. They have congruent corresponding sides.

   In our exercise, we have two parallelograms that have congruent corresponding angles. However, we do not know if their corresponding sides are also congruent. Let's take a look at the example of two parallelograms that have four congruent corresponding angles and do not have congruent corresponding sides.

   

   Looking at the picture, we can say that parallelograms with four congruent corresponding angles do not have to be congruent because the sides can have different lengths. However, we can find an example of two parallelograms with corresponding angles of the same measure that are congruent figures.

   

   Now we know that the parallelograms with four corresponding angles of the same measures can be congruent. Therefore, the parallelograms from our exercise are sometimes congruent.