Chapter 3.3, Problem 2PSA

To determine

To show that two sides are congruent.

Answer to Problem 2PSA

  $\overline{HJ}and\overline{KJ}arecongruent.$

Explanation of Solution

Given information:

  $\begin{array}{l}\angle HGJ \cong \angle KJG\hfill \\ \angle KGJ \cong \angle HJG\hfill \end{array}$

Formula used:

The below property is used:

Two triangles are congruent by ASA congruence rule.

Proof:

From figure, we get

  

It is given that,

  $\begin{array}{l}\angle HGJ \cong \angle KJG\hfill \\ \angle KGJ \cong \angle HJG\hfill \end{array}$

By reflexive property, we get

  $\overline{GJ }\cong \overline{GJ}$

By ASA congruence rule, we get

  $\Delta GHJ \cong \Delta JKG$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{HG} \cong \overline{KJ}$