This worksheet introduces congruence and similarity, teaching students to identify the triangle congruence tests and use a scale factor to solve problems involving similar shapes. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Congruent shapes are exactly the same size and shape — every corresponding side and angle matches exactly.
- Similar shapes are the same shape but not necessarily the same size — corresponding angles are equal, and corresponding sides are in the same ratio (scale factor).
- Triangle congruence tests: sss (all 3 sides), sas (2 sides + included angle), asa (2 angles + included side), rhs (right angle, hypotenuse, one side).
- Two triangles are similar if their corresponding angles are equal (aa test) — this alone is enough, since the third angle is then forced to match too.
- Translations, reflections and rotations always produce a congruent image — they never change size or shape.
What your child will practise:
- Identifying which congruence test (sss, sas, asa, rhs) applies to a given pair of triangles.
- Determining whether two shapes are congruent, similar, both, or neither, from given information.
- Applying a scale factor to find missing side lengths of a similar shape.
- Recalling that area scales with the square of the scale factor, and apply this to similar shapes.
- Explaining why a shape's image under translation, reflection or rotation is always congruent to the original.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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