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 = 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.

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 Shapes

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

7th Grade Math Problems

8th Grade Math Practice

From Angle Angle Side Congruence to HOME PAGE

Recent Articles

• 

1. Rules of Roman Numeration |Roman Number System|Roman Numeration System

   Mar 18, 25 09:41 AM

   
   We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500

   Read More

2. Divisible by 2 | Test of Divisibility by 2 |Rules of Divisibility by 2

   Mar 17, 25 04:04 PM

   
   A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

   Read More

3. Worksheet on 7 Times Table | Printable Multiplication Table | Video

   Mar 17, 25 02:41 PM

   
   Printable worksheet on 7 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

   Read More

4. Worksheet on 6 Times Table | Printable Multiplication Table | Video

   Mar 16, 25 03:09 PM

   
   Printable worksheet on 6 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

   Read More

5. Worksheet on 5 Times Table | Printable Multiplication Table | Video

   Mar 16, 25 01:25 PM

   
   Printable worksheet on 5 times table can be used from everywhere. Homeschoolers can also use these multiplication table sheets to practice at home.

   Read More

Word problems on Pythagorean Theorem