Chapter 4.4, Problem 3CYP

To determine

To prove: $\Delta FGJ\cong \Delta HGJ$

Explanation of Solution

Given information: $\overline{FG}\cong \overline{GH}$ and $\overline{JG}$ bisects $\angle FGH$

  

Proof: The two column proof has been given below.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ \begin{array}{l}\overline{FG}\cong \overline{GH}\\ \angle FGJ=\angle HGJ\\ \overline{FJ}=\overline{HJ}\\ \Delta FGJ\cong \Delta HGJ\end{array}& \begin{array}{l}\text{Given}\\ \text{Angle Bisector Theorem}\\ \overline{JG}\text{bisects}\\ \text{Side-Angle-Side Congruence}\end{array}\end{array}$