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 = 40°, ∠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.
Workedout 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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