Question

1. complete the proof for the base angle theorem. (hint: mark the diagram.)

a. what should be statement 4 and its reason?
b. what should be the reason for step 5?

Explanation:

Step1: Analyze the given information

We have \(PQ = RQ\) (given), \(\angle PQS=\angle RQS\) (\(\overline{QS}\) bisects \(\angle PQR\)), and \(QS = QS\) (reflexive property). These are the conditions for the Side - Angle - Side (SAS) congruence criterion.

Step2: Determine congruent triangles

By the SAS congruence criterion (\(PQ = RQ\), \(\angle PQS=\angle RQS\), \(QS = QS\)), \(\triangle PQS\cong\triangle RQS\).

Answer:

A. Statement 4: \(\triangle PQS\cong\triangle RQS\); Reason 4: Side - Angle - Side (SAS) Congruence Criterion
B. Reason for step 5: Corresponding Parts of Congruent Triangles are Congruent (CPCTC)