Chapter 12.5, Problem 7E

To determine

To show: Whether the congruence statement is true.

Answer to Problem 7E

No, the congruence statement is not 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 $△RST\text{ and }△TQP\text{.}$

Also, $△RST\cong △TQP\text{.}$

Now,

Statements	Reasons
S 1. $\overline{RS}=\overline{PQ}$	Given
S 2. $\overline{ST}=\overline{QT}$	Given
S 3. $\overline{RT}=\overline{PT}$	Given
4. $△RST\cong △PQT$	SSS Congruence Theorem

Therefore, the congruence statement is not true.