# Angle Angle Side Congruence

Conditions for the AAS – Angle Angle Side congruence

Two triangles are said to be congruent if two angles and non- included side of the one triangle is equal to the two angles and the non- included side of the other.

Experiment to prove Congruence with AAS:

Draw a ∆LMN with M = 4, N = 70°, LN = 3 cm.

Also, draw another ∆XYZ with Y = 40°, Z = 70°, XZ = 3cm.

We see that M = Y, N = Z and LN = XZ

Make a trace copy of ∆XYZ and try to make it cover LMN with X on L, Y on M and Z on N. Two triangles cover each other exactly.

Therefore ∆LMN ∆XYZ

Note:

Angle Angle Side (AAS) and Angle Side Angle (ASA) are more or less the same congruence condition.

Worked-out problems on angle angle side congruence triangles (AAS postulate):

1. OB is the bisector of AOC, PM ┴ OA and PN ┴ OC. Show that ∆MPO ∆NPO.

Solution:

In ∆MPO and ∆NPO

PM ┴ OM and PN ┴ ON

Therefore PMO = PNO = 90°

Also, OB is the bisector of AOC

Therefore MOP = NOP

OP = OP common

Therefore, ∆MPO ∆NPO by AAS congruence condition

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Side Angle Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Right Angle Hypotenuse Side congruence

Pythagorean Theorem

Proof of Pythagorean Theorem

Converse of Pythagorean Theorem