Congruent Triangles (Edexcel GCSE Maths)
Revision Note
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Congruent Triangles
What are congruent triangles?
Two triangles are congruent if they are the same size and shape
Although they may be reflections, translations or rotations of each other
All three angles and all three sides must be the same in both triangles
How do I prove that two triangles are congruent?
We only need to show that 3 of the 6 things are the same for both triangles
as long as they are the right three!
To do this we must use one of the 5 standard tests
Name | Description | Diagram |
SAS | Two sides and the angle between them |  |
ASA | Two angles and the side between them |  |
AAS | Any two angles and any side |  |
SSS | All three sides |  |
RHS | The hypotenuse and any other side for a right-angled triangle |  |
Examiner Tips and Tricks
AAA and SSA are not congruent conditions
Worked Example
Prove that triangles ABC and PQR are congruent.
Angle ABC and angle RPQ are both 25°
Angle BAC and angle PRQ are both 90°
Line PR and line AB are both 6cm
Two angles are the same, and the lengths between them are the same
Triangles are congruent by the ASA condition
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