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Given: NQ is the bisector of ∠MNP and ∠NMQ≅∠NPQ Prove: △MNQ≅△PNQ

 Mar 28, 2021
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Since NQ bisects ∠MNP, ∠MNQ = ∠QNP.

 

Considering that ∠NMQ≅∠NPQ, we can create the following diagram:

 

Notice that △MNQ and △PNQ share a side; meaning that we can use the ASA similarity rule to deduce that △MNQ≅△PNQ.

 Mar 28, 2021

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