VC2M8SP04 Official strand: Space

Algorithms for matching shapes

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Build and test clear decisions for congruence and similarity.

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An algorithm compares triangle sides 3, 4, 5 with 6, 8, 10. It finds the same ratio 2 for all corresponding sides. What should it report?

ACongruent because both have three sides. BSimilar but not congruent. CCongruent because ratios exist. DNot similar because the sizes differ.

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Answer: Similar but not congruent.

Every corresponding side is multiplied by 2.
The shared scale factor gives similarity; it is not 1, so the sizes differ.

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Curriculum reference

Victorian Curriculum F–10 Version 2.0

Pi Leo practice scope

Build and test clear decisions for congruence and similarity.

Read the official VCAA curriculum description (VC2M8SP04)

These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.

Activities to practise beyond the quiz

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VC2M8SP04-C01Trace a side-ratio algorithm for triangle similarity.
VC2M8SP04-C02Test and correct decision rules for congruence and similarity.
VC2M8SP04-C03Design, test and explain a geometric classification algorithm.
VC2M8SP04-C04Apply and explain algorithms for matching shapes using calculate and explain each step.
VC2M8SP04-C05Apply and explain algorithms for matching shapes using compare evidence and check a claim.

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Subskills

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Descriptor-derived subskills

D01
Use one consistent scale factorTrace a side-ratio algorithm for triangle similarity.
D02
Try a counterexampleTest and correct decision rules for congruence and similarity.
D03
Calculate and explain each stepApply and explain algorithms for matching shapes using calculate and explain each step.
D04
Compare evidence and check a claimApply and explain algorithms for matching shapes using compare evidence and check a claim.