Congruent Figures

Congruent Figures is a concept in geometry. It's easy to understand and learn concept. At first, you may get confused about all the Angles. However, as you learn it, you will understand the concept of congruent figures. There are many times that the concept of congruent figures is used around you. However, you don't realize that the concept is being used. 


In congruent segments geometry, congruent figures are those figures which have the same shape and dimension. When two objects or characters have the same way and size while sliding or flipping, the objects are said to be congruent shapes.


How to Draw Congruent Figures? 

You can take a sheet of paper and draw two similar figures on it. Cut the figures and place them on one another. Both the statistics will be congruent when you put one picture on top of the other image.


In Geometry, when we say that one (A) figure is equal to figure (B), we write down as figure A ≅ to figure B. Below, you will learn more about congruent shapes, congruent line segments, and corresponding shapes and angles.


How to find The Congruence of two Figures?

To know what are congruent figures you have to keep two plane figures in front of you, and you have to find if they are identical with each other or not. Use the following method to discover if the two figures are congruent figures or not:

  • Take a tracing paper and trace the outline of figure A.

  • Cut out the shape of figure A and place it over the figure B.

  • You can set the paper over figure B or flip it and then put it over figure B.

  • If the two figures completely cover each other, they are congruent to each other. You can symbolically represent it, as figure A is ≅ to figure B.


Congruent Lines Segments

Like two figures can be congruent, so can two lines and lines segments. Two line segments are congruent if they have equal or the same length.


If you want to find out if two figures are corresponding to each other or not, you can use the same method as given above. Take two line segments and place them on top of each other. So, two line segments are congruent if they are equal or the same.


What are Congruent Angles?

Besides, line segments, angles can be congruent to each other too. If angle A and angle B are 36 degrees each, they are congruent. However, if the corners are different, the angles are not congruent with each other.


When two angles have the same measure in degree, they are congruent to each other. The angles may differ in position and orientation on the plane. You can use the method given above to find out the congruency of the angles.


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Here are two triangles with congruent angles. 


If you have two figures, ∠ABC and ∠QPR, with the same angle, which you can assume as 45 degrees, when you use the method given above, you will see that the ∠ABC ≅ ∠QPR means they are congruent to each other.


How to prove if two Angles are Congruent to each other?

There is another way to check for the congruence of two angles. Follow the below-given method to prove that two angles are congruent:


  • When two angles and the side between them are equal or similar in both the triangles, it is an ASA congruence.

  • When two angles and a side that is not between them is identical or identical in both the triangles, it’s an AAS congruence.

  • If three sides of a triangle are the same or equal to each other, it is SSS congruence. 

  • When two hands and one angle between them makes the two triangles congruent, it’s the SAS congruence.

 

Congruent Angles Solved Examples

Here are a few congruent angles solved examples that will help you understand how to find the congruence of two angles.


 Example 1:

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Here are two figures which you need to prove as congruent.


The angles G and S of the diagram above are 42 degrees, which means that they are equal. When two angles of a figure are identical or similar, it means that they are congruent.


 Example 2:

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Here are two figures which you have to prove as congruent. 


The angles of the two figures are 155 degrees each, so It means that R and Q are equal to each other. If two aspects are similar to each other, it means that they are congruent to each other.


Fun Facts About Congruent Shapes

Here are some fun facts about the corresponding figures:

  • Squares that have equal length on all four sides are congruent shapes.

  • An equilateral triangle which has equal distances on all the three sides are congruent.

  • Slices of pizza are a perfect example of a congruent triangle and congruent angles.

  • When you combine two congruent triangles, they form vertical angles at a corner.

  • Most buildings in the United States are congruent triangles.

FAQ (Frequently Asked Questions)

Q1. What is the Congruent Section in Geometry?

A. The congruent section in geometry is when two lines, segments, figures, or angles are equal. Two angles are similar or equal to each other when you keep one over the other and they are equal. Hence, it means that they are congruent to each other.

Q2. In how many ways can you Prove if two Triangles are Congruent to each other?

A. There are four ways in which you can prove that the two angles are equal to each other. One of the ways is to see if three sides of the triangle are equal to each other, then it’s the SSS congruency rule. Another way to prove congruency is to see if two angles are equal to each other and one side is equal. It means that the triangles are congruent due to the ASA congruence. When there are two congruent lines and one congruent angle is equal it means triangles are congruent because of SAS congruence. Lastly, when a non-included side and two angles of two angles are similar to each other with AAS congruence rule.