Chapter 5.2, Problem 10PSA

To determine

To Calculate: The probability for which lines $c\parallel d$ .

Answer to Problem 10PSA

The probability for which lines $c\parallel d$ is 50%, i.e. 0.5.

Explanation of Solution

Given:

  

Either $\angle 1\cong \angle 2\text{or }\angle 1\cong \angle 3$

Concept Used:

When parallel lines is intersected by a transversal alternate interior angles are equal.

Calculation:

Here, we have

  $\angle 1\cong \angle 2$ , which are alternate interior angles.

Since, when parallel lines is intersected by a transversal alternate interior angles are equal.

But

  $\begin{array}{l}\angle 1\cancel{\cong }\angle 3\\ \because \angle 1+\angle 3=180°\end{array}$

Thus, out of three two angles are congruent.

Therefore, the probability for which lines $c\parallel d$ is 50%, i.e. 0.5.