Exercise 1 Page 565

Let's begin with recalling the Vertical Angles Theorem. This theorem tells us that two vertical angles are congruent. In our exercise, this can be applied to state that ∠ YZX=∠ WZV.

Since XY is parallel to VW we can use the Alternate Interior Angles Theorem. According to this theorem, if parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. This means that ∠ ZYX= ∠ ZVW and ∠ ZXY= ∠ ZWV.

Now, let's recall that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This postulate is called Angle-Angle Similarity Theorem. Since the triangles in our example have three congruent angles, we can say that they are similar by AA Similarity Theorem.