Chapter 5.2, Problem 7CE

To determine

To state: whether $ABCD$ must be a parallelogram.

Answer to Problem 7CE

It follows that quadrilateral $ABCD$ is a parallelogram.

Explanation of Solution

Given information:

Given figure,

Calculation:

From the figure note that,

  $\begin{array}{l}AB\parallel DC\\ \angle A=90°\\ \angle B=90°\end{array}$

Since $AB\parallel DC$ , so the sum of adjacent angle is $180°$

  $\begin{array}{c}\angle A+\angle D=180°\\ 90°+\angle D=180°\\ \angle D=90°\end{array}$

In a similar way, find the remaining angle as,

  $\angle C=90°$

This implies that the opposite angles of a quadrilateral $ABCD$ are congruent.

Therefore, it follows that quadrilateral $ABCD$ is a parallelogram.