Chapter 8.6, Problem 48E

To determine

To Find:Is your friend correct?

Answer to Problem 48E

He is correct.

Explanation of Solution

Given: Your friend claims that $\angle TPU\cong \angle QPR$

  

  $\angle QPRand\angle RPS$ are complementary and $\angle SPTand\angle TPU$ are complementary.

Therefore,

  $\begin{array}{l}\angle QPR+\angle RPS=\mathrm{90...}(i)\\ similarly\\ \angle SPT+\angle TPU=\mathrm{90.....}(ii)\\ subtract(i)from(ii)\\ \angle SPT+\angle TPU-\angle QPR+\angle RPS=90-90\\ \angle TPU-\angle QPR=0\\ \angle TPU=\angle QPR\end{array}$

That means

  $\angle TPU\cong \angle QPR$

Hence $\angle TPU\cong \angle QPR$

They are congruent.