Chapter 12.5, Problem 9E

To determine

To show: Whether the congruence statement is true.

Answer to Problem 9E

Yes, the congruence statement is true.

Explanation of Solution

Given information:

  

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,

There are two triangles $△DEF\text{ and }△DGF\text{.}$

Also, $△DEF\cong △DGF\text{.}$

Now,

Statements	Reasons
S 1. $\overline{DE}=\overline{DG}$	Given
S 2. $\overline{EF}=\overline{GF}$	Given
S 3. $\overline{DF}=\overline{DF}$	Reflexive Property of Congruence
4. $△DEF\cong △DGF$	SSS Congruence Theorem

Therefore, the congruence statement is true.