Question

how can I use deductive reasoning to show that

Answer 1

$In\text{ }\Delta PQS\text{ and }\Delta RQS$

$\bar{PQ}\cong\bar{RQ}$$\angle PQS=\angle RQS\text{ (since QS bisects }\angle PQR)$$\bar{QS}=\bar{QS}\text{ (common)}$

Therefore,

$\Delta PQS\cong\Delta RQS\text{ (SAS congruence rule.)}$

So,

$\angle P\cong\angle R$