Pythagoras' Theorem
Year 9 📐 Geometry & Measures Apply Pythagoras in 2D and 3D problems.
📐 Pythagoras' Theorem
In any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
⚡ Pythagoras' Theorem
$$a^2 + b^2 = c^2$$where $c$ is the hypotenuse (longest side, opposite the right angle)
🔢 Finding the Hypotenuse
Example: Right triangle with legs 3 and 4.
$c^2 = 3^2 + 4^2 = 9 + 16 = 25$
$c = \sqrt{25} = 5$ ✓ (the famous 3-4-5 triangle!)
$c^2 = 3^2 + 4^2 = 9 + 16 = 25$
$c = \sqrt{25} = 5$ ✓ (the famous 3-4-5 triangle!)
🔄 Finding a Leg
Finding a Leg
$$a = \sqrt{c^2 - b^2}$$Example: $c = 13$, $b = 5$, find $a$:
$a^2 = 13^2 - 5^2 = 169 - 25 = 144$
$a = \sqrt{144} = 12$
$a^2 = 13^2 - 5^2 = 169 - 25 = 144$
$a = \sqrt{144} = 12$
✅ Pythagorean Triples
These sets of integers always form right triangles:
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
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Interactive Demonstration — Pythagoras' Theorem
📐 Pythagoras Interactive Demo
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