Question

Given that PQ equal to RQ . S is the mid point of PR . what reason can be given to prove that the other two angles ?​

Answer 1

You can use SSS congruence criterion:

In △PQS and △RQS,

PQ = RQ (Given)

SQ = SQ (Common)

PS = RS (Given)

So, △PQS ≅ △RQS by SSS criterion

Now, since they're congruent you can prove that any two of the corresponding angles are equal simply by CPCT