Year 8 - Congruence and similarity - Free practice
Year 8 Congruence & Similarity Worksheets
SSS, SAS, AAS - which conditions prove triangles match?
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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
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About this worksheet
Why we built it
Year 8 introduces the four congruence conditions (SSS, SAS, AAS, RHS) and the corresponding similarity conditions. The hard part is recognising which one applies - these worksheets give your student varied figures to train that instinct.
What's covered
Sub-skills your student will practise
- ✓The four triangle-congruence conditions (SSS, SAS, AAS, RHS)
- ✓Identifying which condition applies to a given figure
- ✓Similar-triangle conditions (AA, SSS, SAS in ratio)
- ✓Using similarity to find missing side lengths
- ✓Short formal proofs of congruence
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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
Rebecca M.
Year 8 · Maths
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Year 9 · Maths
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Ella, student
Year 10 · Maths
Frequently asked
Questions parents ask about congruence and similarity
What's the difference between congruent and similar?
Congruent shapes are exactly the same - same side lengths and angles. Similar shapes have the same angles but their sides are in proportion - one is a scaled version of the other. Photos enlarged on a printer are similar, not congruent.
What are the four triangle congruence conditions?
SSS (three equal sides), SAS (two sides and the angle between them), AAS (two angles and a non-included side), and RHS (right angle, hypotenuse, side). Any one of these is enough to prove congruence.
Why doesn't SSA prove congruence?
Because two triangles can share two sides and a non-included angle yet have different shapes. This is the 'ambiguous case'. RHS works because the right angle removes the ambiguity.
How is similarity used in Year 8?
Mostly to find missing lengths. If two triangles are similar with a ratio of 2:3, every pair of corresponding sides has the same ratio. This sets up trigonometry in Year 9.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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Talk to us about Year 8 congruence and similarity.
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