Question

I need help ASAP!!! Please tell me the answer Congruent Triangle Proof

Answer 1

see explanation

Explanation:

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

NQ is an angle bisector then ∠ MNQ = ∠ PNQ

∠ M = ∠ N , so the triangle is isosceles with 2 equal legs, then

MN = PN

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∠ MNQ = ∠ PNQ

MN = PN ( included sides between the 2 angles )

∠ M = ∠ N

Δ MNQ ≅ Δ PNQ by the ASA postulate

Answer 2

Explanation:

In Δ MNP,

∠NMQ ≅ ∠NPQ

⇒ NM = NP - ------> (I) {Sides opposite to equal angles are equal}

In ΔMNQ & ΔPNQ,

∠MNQ ≅ ∠PNQ {NQ is angle bisector}

NM = NP {from (I)}

∠NMQ ≅ ∠NPQ {Given}

ΔMNQ ≅ ΔPNQ - Angle Side Angle {ASA congruent}