MA30-01 Maths Coming soon
Pythagoras' theorem in two dimensions
This lesson is coming soon.
In this lesson
Apply Pythagoras' theorem to find a missing side of a right-angled triangle, correctly choosing to add or subtract the squares depending on whether the hypotenuse or a shorter side is missing, and recognise when Pythagoras (rather than trigonometry or an area formula) is the right tool.
What it covers
- State Pythagoras' theorem a^2+b^2=c^2 and identify the hypotenuse as the side opposite the right angle
- Find a missing hypotenuse: square both known sides, add, then square root
- Find a missing shorter side: square both known values, subtract the smaller from the larger, then square root
- Check whether a triangle is right-angled by testing whether the longest side squared equals the sum of the other two squares
- A short contrastive moment showing why Pythagoras is the right tool here and not trigonometry (no angle given) or an area formula (asked for a length, not a space)
Key words
For: Cambridge IGCSE 0580, Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Cambridge IGCSE 0580 | C6.1 | Know and use Pythagoras' theorem. |
| Cambridge IGCSE 0580 | E6.1 | Know and use Pythagoras' theorem. |
| Edexcel IGCSE 4MA1 | F4.8A | Know, understand and use Pythagoras' theorem in two dimensions |
| AQA GCSE 8300 | G6 | Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs |
| AQA GCSE 8300 | G20 | Know the formulae for: Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent |
| Edexcel GCSE 1MA1 | G6 | Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs |
| Edexcel GCSE 1MA1 | G20 | Know the formulae for: Pythagoras’ theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two-dimensional figures |
| Eduqas GCSE C300 | FG6 | Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras' Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs |
| Eduqas GCSE C300 | HG6 | Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras' Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs |
| Eduqas GCSE C300 | FG18 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two dimensional figures |
| OCR GCSE J560 | 10.05a | Know, derive and apply Pythagoras' theorem a^2 + b^2 = c^2 to find lengths in right-angled triangles in 2D figures. |
For teachers
This GCSE Maths lesson teaches Pythagoras' theorem in two dimensions. By the end, students should be able to apply Pythagoras' theorem to find a missing side of a right-angled triangle, correctly choosing to add or subtract the squares depending on whether the hypotenuse or a shorter side is missing, and recognise when Pythagoras (rather than trigonometry or an area formula) is the right tool. It works through two worked examples and the mistakes examiners report.