Question

Which postulate or theorem proves that these two triangles are congruent?

Answer 1

ANSWER

postulate or theorem proves that these two triangles are congruent is option (C)

i.e   AAS Congruence Theorem

Reason

AAS Congruence Theorem

In this theorem two angle and one sides of the two triangle are equal.

In ΔMNR and ΔQNP

∠MNR =∠ QNP

( Vertically opposite angle property )

∠RMN = ∠QPN

(Corresponding angle property)

RN = NQ

( As given in the diagram )

therefore

ΔMNR≅ Δ QNP

these triangle are congurent by the  AAS Congruence Theorem.

Hence proved

Answer 2

Answer:

C) AAS Congruence Theorem

Step-by-step explanation:

The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

In this case the congruent angles are: M with P (shown in the figure) and N, which is equal in both triangles because two opposite angles are formed in the intersection of segments MP with RQ.

The congruent non-included sides are RN and NQ (shown in the figure).