Question

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

A. ASA Congruence Postulate
B. AAS Congruence Theorem
C. HL Congruence Theorem
D. SAS Congruence Postulate

Answer 1

B: AAS Congruence Theorem

Answer 2

Option (B)

Explanation:

From the given picture,

Given:

Two lines PM and QR are intersecting each other at a point N.

∠NMR ≅ ∠NPQ

NR ≅ QN

To prove:

ΔMNR ≅ ΔPNQ

Statements Reasons

1). NR ≅ QN 1). Given

2). ∠NMR ≅ ∠NPQ 2). Given

3). ∠MNR ≅ ∠PNQ 3). Definition of vertical angles

4). ΔMNR ≅ ΔPNQ 4). AAS theorem of congruence

Therefore, Option (B) will be the correct option.