Congruent Angles

In congruent angles we will learn how to recognize that when two angles are congruent. 

In case of two angles having the same vertex:

Congruent Angles

Suppose ∠LOM = ∠PON having same vertex O. Now we will verify their congruence.

A straight line QOR is drawn through point O and a perpendicular xy is drawn on QOR at O.

With respect to the axis of reflection xy, ∠P’ON’ is the image of ∠PON. Now with centre of rotation O, OP’ is rotated through such an angle in anticlockwise direction, so that OP’ coincides with OM. Since ∠P’ON’ is rigid figure and equal to ∠LOM, ON’ falls on OL.

Therefore, ∠LOM ≅ ∠N’OP’ ≅ ∠NOP = ∠PON

Congruent Angle

With O as center of rotation, OP is rotated through such an angle (in anticlockwise direction) so that OP lies on OL. In the same manner ON being rotated equally, falls on OM.

Therefore, ∠LOM ≅ ∠PON


If two equal angles are at different positions but lie on the same plane.

Congruent Angles Image

∠LMN and ∠PQR are two equal angles at different positions but lie on the same plane.

Angles Sharing Common Vertex

Taking xy, the perpendicular bisector of MQ as the axis of reflection, the image of ∠PQR is ∠P’MR’.

Therefore, ∠P’MR’ ≅ ∠PQR

Now observe that ∠LMN and ∠P’MR’ are two equal angles sharing common vertex M.

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 congruent angles 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. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More

Word problems on Pythagorean Theorem