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MathidiaMathematics Academy
Similarity and congruence
Lesson 41 of 75
Introduction

Congruent shapes

Objective. Identify congruence and justify matching vertices and sides.

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

Learn: the key idea

Congruent shapes are identical in both size and shape, meaning one can be placed exactly on top of the other using rotation, reflection or translation alone, without resizing. To prove two triangles are congruent, one of several standard conditions must be met: 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). When justifying congruence, matching vertices must be stated in the same corresponding order, such as triangle ABC being congruent to triangle DEF, so angle A matches angle D. Simply looking similar is not enough; a specific condition must be demonstrated with matching measurements.

Worked example

Triangle ABC has sides AB = 5 cm, BC = 7 cm and angle B = 60°. Triangle DEF has sides DE = 5 cm, EF = 7 cm and angle E = 60°. State which congruence condition proves these triangles are congruent.

Diagram of a triangle
  1. 1Compare the given sides: AB = DE = 5 cm and BC = EF = 7 cm.
  2. 2Compare the given angles: angle B = angle E = 60°.
  3. 3The equal angle (B and E) lies between the two equal sides in each triangle.
  4. 4This matches the SAS (side-angle-side) condition for congruence.

Answer: SAS (side-angle-side)

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Practice

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Common mistake. Pupils sometimes claim triangles are congruent because they 'look the same size' without checking a specific condition like SSS or SAS using actual given measurements. Always identify which congruence condition applies using matched sides and angles.

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