Question

in exercises 1 - 6, decide whether it is possible to prove that the triangles are congruent. if it is possible, state the theorem or postulate you would use. explain your reasoning. (lessons 4.3 and 4.4)

Explanation:

Step1: Identify the corresponding parts

In \(\triangle SPQ\) and \(\triangle SRQ\), \(SP = SR\) (given by the double - tick marks), \(PQ=RQ\) (given by the single - tick marks), and \(SQ = SQ\) (common side).

Step2: Apply the congruence theorem

By the Side - Side - Side (SSS) congruence theorem, if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Answer:

It is possible to prove that \(\triangle SPQ\cong\triangle SRQ\). We use the SSS (Side - Side - Side) congruence theorem.