Chapter 6, Problem 8RP

a

To determine

To Check:The $\angle \text{APQ \&}\angle \text{BPQ}$ are congruent.

Answer to Problem 8RP

The angles are congruent or the statement is true.

Explanation of Solution

Given information A circle with center O

One given line $\overleftrightarrow{\text{PQ}}\perp \text{m}$

Two points A & B are on circle

Since given points A and B are on circle

Thus, $\angle \text{APQ=}\angle \text{BPQ=90}°$

  $\angle \text{APQ}\cong \angle \text{BPQ, by definition of congruency}$

Hence, true

b

To determine

To check: The given two-line segments are congruent or not.

Answer to Problem 8RP

Two given lines are congruent or the statement is true.

Explanation of Solution

Given information A circle with center O

One given line $\overleftrightarrow{\text{PQ}}\perp \text{m}$

Two points A & B are on circle

Given line segments $\overline{\text{AP}}=\overline{\text{PB,}}\text{ since, given line segments are radii of given circle}$

Thus, $\overline{\text{AP}}\cong \overline{\text{PB}},\text{by definition of congruency}$

Hence, true

c

To determine

To check:The given line segment QP is perpendicular to AB.

Answer to Problem 8RP

The given line segment will not be perpendicular to each other or the statement is false.

Explanation of Solution

Given information A circle with center O

One given line $\overleftrightarrow{\text{PQ}}\perp \text{m}$

Two points A & B are on circle

Since, $\overleftrightarrow{\text{PQ}}\perp \text{m}$ …. Given

and line segment AB does not belong to the foot of line QP

Thus, $\overleftrightarrow{\text{QP}}\text{ will not be perpendicular to }\overline{\text{AB}}$

Hence, false