Chapter 7.2, Problem 7PSA

To determine

To prove : VBYZ is a parallelogram.

Explanation of Solution

Given information : The following information has been given

  $\angle A=\angle X$

  $\angle AVZ=\angle XYB$

  $\angle ZVY=\angle YBX$

Formula used : Information/data provided in the question that are used to solve this particular category of solution/solution.

Proof : We know that

  $\angle ZVY=\angle YBX$

Thus, we can say that ZV and YB are parallel lines

Now, we use

  $\angle A=\angle X$

  $\angle AVZ=\angle XYB$

Thus, triangles AZV and XBY are similar triangles

Now, we know that as ZV and YB are parallel lines with all similar angles,

  $\overrightarrow{ZV}\cong \overrightarrow{YB}$

Hence, opposite lines are parallel and equal − thus, VBYZ has to be a parallelogram