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MathidiaMathematics Academy
Similarity, congruence and scale
Lesson 46 of 75
Introduction

Triangle congruence

Objective. Prove congruence using SSS, SAS, ASA and RHS.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Triangle congruence means two triangles are identical in shape and size, provable using one of four standard criteria: SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), or RHS (right angle, hypotenuse and one other side equal, for right-angled triangles only). To prove congruence, identify matching pairs of sides or angles between the triangles and state which criterion applies, such as "AB=DE, BC=EF, angle B=angle E, so SAS". Always state the criterion explicitly rather than just showing the shapes look similar. The order of vertices in the congruence statement should match corresponding points, for example triangle ABC≅triangle DEF implies A matches D, B matches E and C matches F.

Worked example

Triangle ABC has AB=7cm, BC=9cm and angle B=50°. Triangle DEF has DE=7cm, EF=9cm and angle E=50°. State which congruence criterion proves the triangles are congruent.

Diagram of a triangle
  1. 1Compare sides: AB=DE=7cm and BC=EF=9cm
  2. 2Compare angles: angle B=angle E=50°, which lies between the two given sides in each triangle
  3. 3Two sides and the included angle match in both triangles
  4. 4This matches the SAS congruence criterion

Answer: SAS

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Practice

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Common mistake. Pupils claim congruence using two sides and a non-included angle (SSA), which is not a valid congruence criterion since it can produce two different triangles. Always check the angle given is between the two known sides (SAS) or use a genuinely valid criterion like ASA or RHS.

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