Chapter 12.5, Problem 4E

To determine

To show: Whether enough information is given to prove that the triangles are congruent using the SSS Congruence Theorem.

Answer to Problem 4E

No, the information is not enough to prove that two triangles are congruent.

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 $△PQS\text{ and }△RQS\text{.}$

Now,

Statements	Reasons
S 1. $\overline{PQ}=\overline{RQ}$	Given
S 2. $\overline{QS}=\overline{QS}$	Reflexive Property of Congruence

Since, the question does not mentioned the third side. We cannot show that the two triangles are congruent.

Hence, the information is not enough to prove that the two triangles are congruent.