△MNQ ≅ △PNQ by SAS congruence theorem.
What is the SAS Congruence Theorem?
If two triangles are congruent by the SAS congruence theorem, then they have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
∠MNQ ≅ ∠PNQ [congruent angles formed by angle bisector]
Therefore, opposite sides to the angles, MQ and PQ would also be congruent.
Thus, MQ ≅ PQ
NQ ≅ NQ [reflexive property]
This means that both triangles have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
Thus, △MNQ ≅ △PNQ by SAS congruence theorem.
Learn more about the SAS congruence theorem on:
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