Chapter 2.7, Problem 15PSB

To determine

To prove : The congruency of $\angle A\cong \angle D$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle A={90}^0$

  $\angle B={90}^0$

  $\angle B=\angle D$

Formula used : Adjacent angles of a parallelogram are supplementary

Proof : We are given that $\angle B=\angle D$

Hence, we can say that the quadrilateral is a parallelogram

Now, we know that the adjacent angles of a parallelogram are supplementary

Thus, we can say that

  $\angle A+\angle D={180}^0$

Now, as $\angle A={90}^0$ , we can say that

  $\angle D={90}^0$

Clearly, we note that $\angle A\cong \angle D$

Hence, the desired congruency is proved