Congruence: conditions for congruent triangles
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Explainer Video
Summary
Congruence: conditions for congruent triangles
In a nutshell
Congruent shapes are shapes that are exactly the same apart from rotational/mirror differences. There are four main conditions for two triangles to be congruent.
Congruency
Two shapes are congruent if they have the same side lengths and the same angles. It doesn't matter if the shapes are rotated slightly differently or if they're mirrored.
Congruency conditions
There are four ways to prove that two triangles are congruent.
name | description | example |
| SSS | All three sides of the triangle are the same |  |
| SAS | Two sides and the angle between them are the same |  |
| AS | Two angles and a corresponding side are the same |  |
| RHS | Both triangles have a right-angle, the same hypotenuse and other common side |  |
Example 1
Are the two triangles shown congruent to one another?
At first glance, the two triangles look to be congruent due to the ASA rule - both triangles have angles of and and they both have a side of .
However, upon closer inspection, this is not a case of ASA. This is because the two sides aren't corresponding.
The triangle to the left has a side length of that is between the two angles of and .
The triangle to the right has a side length of that is not between the two angles of and , so it's not the corresponding sides that are equal.
The triangles are NOT congruent.
FAQs - Frequently Asked Questions
What are the four ways to prove two triangles are congruent?
SSS, SAS, ASA and RHS are the four ways to prove two triangles are congruent.
What does it mean for two shapes to be congruent?
Two shapes are congruent if they are exactly the same shape, just rotated and/or mirrored.