Chapter 6.2, Problem 7CYU

To determine

To prove: $\angle B,\angle C$ and $\angle D$ are right angles.

Explanation of Solution

Given information: $\angle A$ is a right angle.

Proof: By the definition of a parallelogram, $\overline{AB}\parallel \overline{CD}$ . As $\angle A$ is a right angle, then $\overline{AC}\perp \overline{AB}$ . Since perpendicular lines for a right angle, then $\angle C$ is a right angle. As opposite angles in a parallelogram are congruent, then $\angle B\cong \angle C$ and $\angle A\cong \angle D$ which follows $\angle C$ and $\angle D$ are right angles because all right angles are congruent.