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**0°**, ∠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

**Conditions for the Congruence of Triangles**

**Right Angle Hypotenuse Side congruence**

**Converse of Pythagorean Theorem**

**7th Grade Math Problems**

**8th Grade Math Practice**

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