Chapter 2.4, Problem 7PSA

To determine

To Prove: $\angle FKG\cong \angle HJG$

Explanation of Solution

Given information: $\angle FKJ={90}^{\circ },\angle HJK={90}^{\circ },\angle GKJ\cong \angle GJK.$

  

  $\angle FKJ=\angle HJK$ (Each equal to ${90}^{\circ }$ )

  $\therefore \angle FKG+\angle GKJ=\angle GJH+\angle GJK$

Given that $\angle GKJ=\angle GJK$

  $\begin{array}{l}\therefore \angle FKG+\angle GJK=\angle GJH+\angle GJK\\ \therefore \angle FKG=\angle HJG\end{array}$