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. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  2. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  3. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  4. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

  5. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

Word problems on Pythagorean Theorem