Proof summary

Key learning points

• Identity proof: start from one side and reach the other (or show both equal a third expression).
• Geometric proof: state equal angles/lines with theorem names.
• Counter-examples disprove universal claims quickly.

Worked example 1 — Odd + odd

Prove the sum of two odds is even.

Working

Algebraic parity.

Worked example 2 — Consecutive product

Show $n(n+1)$ is even.

Working

Consecutive integers.

Worked example 3 — Square difference

Expand $(n+1)^2-n^2$.

Working

Next odd number.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.