Congruent Triangles (Edexcel GCSE Maths)

Revision Note

Dan Finlay

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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
Side Angle Side

Two sides and the angle between them

SAS triangle

ASA
Angle Side Angle

Two angles and the side between them

ASA triangle

AAS
Angle Angle Side

Any two angles and any side

AAS triangle

SSS
Side Side Side

All three sides

SSS triangle

RHS
Right-angle Hypotenuse Side

The hypotenuse and any other side for a right-angled triangle

RHS triangle

 

Examiner Tips and Tricks

  • AAA and SSA are not congruent conditions

Worked Example

Prove that triangles ABC and PQR are congruent.

congruent-triangle-we

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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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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