Chapter 3.2, Problem 42HP

To determine

To find: The relationship between line $b$ and $c$ .

Answer to Problem 42HP

The relationship between $b$ and $c$ are perpendicular lines.

Explanation of Solution

Given information:

The given information is line $a$ is parallel to line $b$ and $\angle 1\cong \angle 2$ .

Calculation:

Angle $\angle 1$ and angle $\angle 2$ form a linear pair. Since they are congruent, they both must measure $\frac{180}{2}=90$ . Since line $a$ is parallel to line $b$ , then angles $\angle 5$ and $\angle 6$ must each measure $90$ by the corresponding angles postulates. Therefore, lines $b$ and $c$ are perpendicular lines by the definition of perpendicular lines.

Therefore, the relationship between $b$ and $c$ are perpendicular lines.