Chapter 4, Problem 15CUR

To determine

Find that which lines can be proved parallel.

Answer to Problem 15CUR

  $a\parallel b$

Explanation of Solution

Given:

  

  $\angle 8\text{ and }\angle \text{5}$ are right angles.

Calculation:

  $\begin{array}{l}m\angle 5+m\angle 6=180°\mathrm{................}[\text{linear angles]}\\ \Rightarrow m\angle 6+90°=180°\\ \Rightarrow m\angle 6=180°-90°\mathrm{.................}[\text{subtract 90}°\text{ from each side]}\\ \Rightarrow m\angle 6=90°\end{array}$

So, $\angle 8\cong \angle 6$ and they are corresponding angles , where c is the transversal .

So, by Converse of Corresponding Angles Theorem, which states that if any pair of corresponding angles is congruent , then the two lines are parallel.

So, $a\parallel b$