Pythagoras' Theorem — O/L Mathematics

What must I remember about Pythagoras' Theorem?

• Pythagoras' Theorem: In any right-angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
• Algebraic formula: a² + b² = c², where c is the hypotenuse (the longest side opposite the 90° angle), and a, b are the adjacent legs.
• Converse of Pythagoras' Theorem: If the square of the longest side of a triangle equals the sum of the squares of the other two sides (c² = a² + b²), then the angle opposite the longest side is a right angle (90°).
• Pythagorean triples: Primitive integer triples satisfying a² + b² = c² (e.g., 3-4-5, 5-12-13, 7-24-25, 8-15-17, 9-40-41) and their scalar multiples.
• Three-dimensional application: Diagonal of a rectangular cuboid: d = √(l² + w² + h²).

Test yourself (1 minute)

1. Hypotenuse identification

   The hypotenuse is ALWAYS the side opposite the right angle; when calculating a shorter leg, SUBTRACT: a² = c² - b².

2. Converse proof structure

   To prove ∠C = 90°, evaluate c² independently, evaluate a² + b² independently, show they are equal, then conclude 'by converse of Pythagoras' theorem'.

3. Surd and exact form

   If an answer does not result in an exact integer, express it in simplified surd form (e.g., √50 = 5√2) or round to requested decimal places.

Practise Pythagoras' Theorem questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 17)

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Where does Pythagoras' Theorem fit in the syllabus?

Grade 11 · Term 2