Chapter 1.5, Problem 15PSA

To determine

To Prove: $\overrightarrow{HK}\text{ bisects}\angle FHJ$

Explanation of Solution

Given:

  

  $\angle 1\cong \angle 2$

Concept Used:

Bisector of an angle divides into equal parts.

Proof:

Here, we have

  $\begin{array}{l}\angle 1\cong \angle 2\\ \Rightarrow \angle FHK\cong \angle KHJ\\ \Rightarrow m\angle FHK=m\angle KHJ\\ \Rightarrow m\angle 1=m\angle 2\\ \Rightarrow \overrightarrow{HK}\text{ bisects}\angle FHJ\end{array}$