Pass Check: Pythagoras' Theorem
a^2 + b^2 = c^2 for right-angled triangles only; c is always the hypotenuse.
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Pythagoras' theorem
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Pythagorean triple
A set of three whole numbers satisfying a^2 + b^2 = c^2, e.g. 3, 4, 5.
3D Pythagoras
Applying the theorem twice (or once in 3D form) to find a diagonal through a cuboid.
Quick check
Mixed quiz
1. A right-angled triangle has shorter sides 9 cm and 12 cm. Find the hypotenuse.
2. A right-angled triangle has shorter sides 7 cm and 24 cm. Find the hypotenuse.
3. A right-angled triangle has hypotenuse 17 cm and one shorter side 8 cm. Find the other shorter side.
4. A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse.
5. A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
6. A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the other shorter side.
7. A right-angled triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.
8. A right-angled triangle has hypotenuse 5 cm and one shorter side 3 cm. Find the other shorter side.