Chapter 2, Problem 24RP

To determine

To Prove: The congruency of $\angle F$ with respect to $\angle J$

Explanation of Solution

Given information: $\angle F\cong \angle 1$

  $\angle J\cong \angle 2$

  $\overline{FK}\perp \overline{KH}$

  $\overline{GK}\perp \overline{KJ}$

Proof: Here, $\angle FKG+\angle GKH={90}^{\circ }$

And, $\angle JKH+\angle HKG={90}^{\circ }$

  $\angle FKG+\angle GKH=\angle JKH+\angle HKG$

  $\angle 1=\angle 2$

And, $\angle F\cong \angle 1$ and $\angle J\cong \angle 2$ (given)

So that, $\angle F\cong \angle J$