Geometric Proof

Build justified arguments using angle facts, parallel lines and triangle congruence.

Curriculum rangeYears 8–11

The blue angle is given as 65°. Pick a relationship to find the pink angle -- and see why.

Learning notes

Geometric Proof essentials

Keep these rules beside you while you explore and practise.

A proof is a connected chain of statements supported by known facts, definitions or earlier results.

\text{Corresponding}=\text{equal}\qquad\text{Alternate}=\text{equal}

\text{Co-interior angles}=180^\circ

The accepted conditions are SSS, SAS, ASA/AAS and RHS. AAA proves similarity, not congruence.

Once triangles are congruent, corresponding sides and angles are equal.

\triangle ABC\cong\triangle DEF

💡Proof habit: name the theorem or angle fact explicitly; a diagram alone is not a reason.