Chapter 15, Problem 8RP

To determine

To Prove: In the given figure the segment PS is greater than QR.

Explanation of Solution

Given:

  

  $\overrightarrow{PQ}\cong \overrightarrow{RS}$

Formula Used:

  $\text{Relative property of congruence and SAS inequality theorem}\text{.}$

Calculation:

  $\begin{array}{l}PR=PR\left(\text{reflexive property of congruence}\right)\\ \angle 2<\angle 1\left(\text{exterior angle is larger than its two remote angles}\right)\\ PS>QR\left(SAS\text{ inequality theorem}\right)\\ \text{hence proved}\text{.}\end{array}$

Conclusion:

Thus, $\text{The relationship in given }\Delta \text{ is proved}\text{.}$