Chapter 12.5, Problem 15E

To determine

To proof: $△LMJ\cong △JKL$

Explanation of Solution

Given information:

  $\overline{LM}\cong \overline{JK},\overline{MJ}\cong \overline{KL}$

  

Formula used:

Side-Side-Side Congruence Theorem

If three sides of one triangle are congruent to three sides of a second triangle, then two triangles are congruent.

Calculation:

According to the question,

We have two triangles:-

  

Triangles $△LMJ\text{ and }△JKL\text{.}$

Now,

Statements	Reasons
S 1. $\overline{LM}=\overline{JK}$	Given , $\overline{LM}\cong \overline{JK}$
S 2. $\overline{MJ}=\overline{KL}$	Given, $\overline{MJ}\cong \overline{KL}$
S 3. $\overline{LJ}=\overline{JL}$	Reflexive Property of Congruence
4. $△LMJ\cong △JKL$	SSS Congruence Theorem

Hence proved.