Chapter 12.5, Problem 8E

To determine

To show: Whether the congruence statement is true.

Answer to Problem 8E

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 $△ABD\text{ and }△CDB\text{.}$

Also, $△ABD\cong △CDB\text{.}$

Now,

Statements	Reasons
S 1. $\overline{AB}=\overline{CD}$	Given
S 2. $\overline{BD}=\overline{DB}$	Reflexive Property of Congruence
S 3. $\overline{AD}=\overline{CB}$	Given
4. $△ABD\cong △CDB$	SSS Congruence Theorem

Therefore, the congruence statement is true.