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Similar-triangle scale factors and lengths · Check your progress
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Similar-triangle scale factors and lengths · Retention check
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Practise: Similar-triangle scale factors and lengths
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Revision notes
Prove congruence, similarity, circle, midpoint and tangent–chord relationships, state the conditions each step needs and test claims with counterexamples.
Key ideas
- Congruence, similarity and circle proofs
Choose the triangles that contain the target, justify congruence or similarity with exact correspondences and use circle properties only in their stated configurations.
- Midpoint and tangent–chord proofs
Derive midpoint relationships, distinguish alternate segments and build a non-circular proof with a missing-condition counterexample.
From the G3 Additional Mathematics 2027 syllabus
- Properties of parallel lines cut by a transversal, perpendicular and angle bisectors, triangles, special quadrilaterals and circles
- Congruent and similar triangles
- Midpoint theorem
- Tangent-chord theorem (alternate segment theorem) (The first two properties are learnt in G3 Mathematics.)