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.

Angle Angle Side Congruence

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.

Angle Angle Side Congruence Triangles

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




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Comparing and Ordering Decimals |Arranging Decimals

    Apr 19, 25 12:16 PM

    Arranging Decimals
    Practice different types of math questions given in the worksheet on comparing and ordering decimals. This worksheet contains questions mainly related to compare decimals and then place the decimals i…

    Read More

  2. Comparison of Decimal Fractions | Comparing Decimals Numbers | Decimal

    Apr 19, 25 11:47 AM

    Comparison of Decimal Fractions
    While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the…

    Read More

  3. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Apr 19, 25 11:25 AM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  4. Missing Numbers up to 10 | Worksheets on Missing Numbers up to 10

    Apr 18, 25 04:53 PM

    missing numbers up to 10
    Printable worksheets on missing numbers up to 10 help the kids to practice counting of the numbers.

    Read More

  5. Ordering Decimals | Comparing Decimals | Ascending & Descending Order

    Apr 18, 25 01:49 PM

    Ordering Decimal Numbers
    In ordering decimals we will learn how to compare two or more decimals. (i) Convert each of them as like decimals. (ii) Compare these decimals just as we compare two whole numbers ignoring

    Read More

Word problems on Pythagorean Theorem