Question

Which postulate or theorem proves △MNQ≅△PNQ ?

Answer 1

Angle Angle Side Congruence Theorem proves ΔMNQ = ΔPNQ.

Answer 2

To find the congruence of two triangles there are 5 different postulates.

These are

1. Side, Side, Side (SSS)

2. SIde, Angle, Side (SAS)

3. Angle, Side, Angle (ASA)

4. Angle, Angle, Side (AAS)

5. Hypotenuse, Leg (HL)

In the given figure,

angle M of triange MNQ is equal to the angle P of triangle PNQ,

angle N of triangle MNQ is equal to the angle N of triangle PNQ which is right angle

and both the triangle share a common side that is NQ,

Hence by AAS (angle angle side ) postulate both the triangle is congruent .

That is triangle MNQ is congruent to triangle PNQ