Chapter 3, Problem 7SGR

To determine

To Find: The weather each of the sentence is true or false and replace the underlined word or make the sentence true if the sentence is false.

Answer to Problem 7SGR

The given statement is false and the correct statement is If $p\left|\right|q$ , then $\angle 2$ and $\angle 8$ are congruent.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

If $p\left|\right|q$ , then $\angle 2$ and $\angle 8$ are supplementary.

Calculation:

Consider that for $p\left|\right|q$ then $\angle 2\cong 6$ as the corresponding are equal as they are formed by the pair of the transversal lines so the transversal are congruent. Consider that $\angle 6\cong \angle 8$ as the vertical angles are congruent then by the transverse property $\angle 2\cong \angle 8$ .

Thus, the given statement is false and the correct statement is If $p\left|\right|q$ , then $\angle 2$ and $\angle 8$ are congruent.