Chapter 3.3, Problem 9PSA

To determine

To show two sides are congruent.

Answer to Problem 9PSA

  $\overline{FG}and\overline{FJ}arecongruent.$

Explanation of Solution

Given information:

  $\overleftrightarrow{FH}bisects\angle GFJand\angle GHJ.$

It is given that,

  $\overleftrightarrow{FH}bisects\angle GFJand\angle GHJ.$

Formula used:

The below properties are used:

If a segment bisects an angle, it divides it into two congruent angles.

Two triangles are congruent by ASA congruence rule.

Proof:

  

If a segment bisects an angle, it divides it into two congruent angles.

  $\angle 2 \cong \angle 1$

  $\angle 3 \cong \angle 4$

By Reflexive property,

  $\overline{FH}\cong \overline{FH}$

By ASA congruence rule, we get

  $\Delta GFH \cong \Delta JFH$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{FG} \cong \overline{FJ}$