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Mathematics · Year 10 · Path · MA5-GEO-P-02

Properties of Geometrical Figures C

Euclidean geometry is an argument, not a set of facts. Five lessons build the discipline of formal proof: what may serve as a reason, how congruence and similarity are established, and how every property and every test is earned from a definition.

5lessons
9syllabus points
3-4hstudy
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1
What a Proof Is, and What a Definition Is
Reasons that count and reasons that do not; a definition as minimum information
2
Formal Congruence Proofs
SSS, SAS, AAS and RHS; why AAA and SSA are not tests; matching vertex order
3
Formal Similarity Proofs
AA, SSS and SAS in ratio; scale factor; similar triangles hidden in one figure
4
Proving Properties of Triangles and Quadrilaterals
Base angles, parallelogram properties, and why a converse needs its own proof
5
Tests for Quadrilaterals and Solving Problems
Tests as converses of properties; disproof by counterexample; combined problems

Focus Area Snapshot

5lessons
9syllabus points
15worked examples
40questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Advanced and Extension in Year 11. Formal proof is the habit senior mathematics assumes you already have, so the setting out matters as much as the geometry.

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