Chapter 15, Problem 16RP

To determine

To Prove: In the given figure required one of angle is smaller than another.

Explanation of Solution

Given:

  $\text{In a given }\Delta \angle \text{PQR<}\angle \text{SRQ }$

  

  $\frac{PR}{PQ}\frac{<}{\cong }\frac{QS}{SR}$

Formula Used:

Reflexive Property of Congruence: It states that in any figure its side is always congruent to itself.

  $\text{Property of Congruence}\text{.}$

Calculation:

  $\begin{array}{l}\text{by reflexive property of congruence}\\ QR=QR\\ bySSS\text{ inequality theorem}\\ \angle PQR<\angle SRQ\\ \text{Hence Proved}\text{.}\end{array}$

Conclusion:

Hence, $\text{Proved}\text{.}$