Congruent shapes

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Proportion


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Summary

Congruent shapes

In a nutshell

Congruent shapes are shapes which are exactly the same. There are four conditions to identify congruent triangles. 



Congruent shapes

Shapes will be congruent if they are exactly the same, which means all the angles and all the side lengths between the shapes will be equal. This also means that shapes will still be congruent even if a shape is rotated, translated or reflected. 


Example 1

Identify whether the two shapes on the grid below are congruent.


Maths; Properties of shapes; KS3 Year 7; Congruent shapes


At first glance, both shapes appear to be a square. 


Using the grid you can count the side lengths of each shape. 

The side lengths of Shape BB​ are all 22 units long. 

The side lengths of Shape BB'​ are also all 22 units long. ​


Using the grid lines identify the angles of each shape. 

As the grid lines are perpendicular to each other, and the sides of both shapes follow the grid lines, all the angle in each shape must be a right angle. 


Both shapes are squares, where each corresponding side is the same length and all the corresponding angles are the same size.


Therefore, shape B and shape B' are congruent.



Congruent triangles

There are four ways to identify whether two triangles are congruent.


NAME

DESCRIPTION

EXAMPLE

SSSSSS​​

All three sides of the triangle are the same

Maths; Properties of shapes; KS3 Year 7; Congruent shapes

SASSAS​​

Two sides and the angle between them are the same

Maths; Properties of shapes; KS3 Year 7; Congruent shapes

ASAASA​​

Two angles and a corresponding side are the same

Maths; Properties of shapes; KS3 Year 7; Congruent shapes

RHSRHS​​

Both triangles have a right-angle, the same hypotenuse and other common side

Maths; Properties of shapes; KS3 Year 7; Congruent shapes



Example 2

Are the two triangles shown congruent to one another?


Maths; Properties of shapes; KS3 Year 7; Congruent shapes


At first glance, both triangles have the angles of 4040^\circ and 8080^\circ and they both have a side of 2.2cm2.2cm. This fits the ASAASA rule of congruence.


However, this is not the case because the two labelled sides are not corresponding.

The triangle to the left has a side length of 2.2cm2.2cm which is between the two angles of 4040^\circ and 8080^\circ.

The triangle to the right has a side length of 2.2cm2.2cm which is not between the two angles of 4040^\circ and 8080^\circ.


Therefore, the triangles are not congruent.


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Exercises

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FAQs - Frequently Asked Questions

What transformations will maintain the congruence of shapes?

What does it mean for two shapes to be congruent?

What are the four ways to prove two triangles are congruent?

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