Chapter 6.2, Problem 38PPS

(a)

To determine

To find: The angle which is congruent to $\angle A$ .

Answer to Problem 38PPS

The following angles are congruent to $\angle A$ ,

• $\angle C$
• $\angle G$
• $\angle E$

Explanation of Solution

Given information: $ABCD$ and $DEFG$ are congruent parallelogram.

The following angles are congruent to $\angle A$

• $\angle C$ is congruent to $\angle A$ because opposite angles of a parallelogram are congruent.
• $\angle G$ is congruent to $\angle A$ because $ABCD\cong DEFG$
• $\angle E$ is congruent to $\angle G$ because opposite angles of a parallelogram are congruent and by Transitive property of Congruence, congruent with $\angle A$ .

(b)

To determine

To find: The sides which is congruent to $\overline{BC}$ .

Answer to Problem 38PPS

The following sides are congruent to $\overline{BC}$ ,

• $\overline{AD}$
• $\overline{DE}$
• $\overline{GF}$

Explanation of Solution

Given information: $ABCD$ and $DEFG$ are congruent parallelogram.

The following sides are congruent to $\overline{BC}$ ,

• $\overline{AD}$ is congruent to $\overline{BC}$ because opposite sides of a parallelogram are congruent.
• $\overline{DE}$ is congruent to $\overline{BC}$ because $\overline{ABCD}\cong \overline{DEFG}$
• $\overline{GF}$ is congruent to $\overline{DE}$ because opposite sides of a parallelogram are congruent and by Transitive property of Congruence, congruent with $\overline{BC}$ .

(c)

To determine

To find: The angles which are supplementary to $\angle C$ .

Answer to Problem 38PPS

The following angles are supplementary to $\angle C$ ,

• $\angle ABC,\angle ADC$
• $\angle GDE,\angle GFE$

Explanation of Solution

Given information: $ABCD$ and $DEFG$ are congruent parallelogram.

The following angles are supplementary to $\angle C$ ,

• $\angle ABC\&\angle ADC$ are supplementary to $\angle C$ because consecutive angles of a parallelogram are supplementary.
• $\angle GDE$ forms vertical angles with $\angle ADC$ . $\angle ADC$ is $\angle GFE$ so they are congruent. By Transitive property of Congruence, both $\angle GDE\&\angle GFE$ are supplementary to $\angle C$ .