Chapter 9, Problem 20CUR

To determine

To prove: ABCD is a rectangle

Explanation of Solution

Given information: In a parallelogram, $\overline{AB}\perp \overline{BC}$

Proof:

Assume that ABCD is not a rectangle.

  

It’s given that ABCD is a parallelogram.

A parallelogram in which one angle is equal to $90°$ is a rectangle.

So, $\overline{AB}$ cannot be perpendicular to $\overline{BC}$ because then ABCD becomes a rectangle.

But it is a contradictionthat $\overline{AB}\perp \overline{BC}$ .

Therefore,

Our assumption is wrong.

ABCD is a rectangle.