Chapter 12.6, Problem 18E

To determine

To Show: The triangle is congruent according to the pattern ASA.

Answer to Problem 18E

The required property has been proved.

Explanation of Solution

Given information:

The figure is given by,

  

The properties are given as, $\overline{AJ}\cong \overline{KC}$ , $\angle BJK\cong \angle BKJ$ , and $\angle A\cong \angle C$ .

It is given that $\overline{AJ}\cong \overline{KC}$ .

This implies that $JK=JK$ by reflexive property of equality.

This implies that $AK=JC$ by addition property of equality.

This implies that $\overline{AK}\cong \overline{CJ}$ by the definition of congruent segments.

It is given that $\angle BJK\cong \angle BKJ$ and $\angle A\cong \angle C$ .

So, the triangle follows the ASA pattern. That means $\Delta ABK\cong \Delta CBJ$ .

Therefore, the required property has been proved.