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:
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
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.
∠LMN and ∠PQR are two equal angles at different positions but
lie on the same plane.
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.
Conditions for the Congruence of Triangles
Right Angle Hypotenuse Side congruence
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.
Recent Articles
-
3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans
Jan 14, 25 01:05 AM
In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie… -
Facts about Subtraction | Subtraction of Small Numbers|Solved Examples
Jan 14, 25 12:29 AM
The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction wit… -
Word Problems on Subtraction |Worksheet on Subtraction Word Problems |
Jan 14, 25 12:21 AM
In word problems on subtraction we need to read the question carefully and understand what we need to find out. We know, in subtraction the larger number from which we subtract the other number (the s… -
Worksheet on Estimating Sums and Differences | Find the Estimated Sum
Jan 13, 25 01:34 PM
In 4th grade worksheet on estimating sums and differences, all grade students can practice the questions on estimations.This exercise sheet on estimating sums and differences can be practiced -
Worksheet on Mixed Addition and Subtraction | Questions on Addition
Jan 12, 25 02:14 PM
In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together.
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.