Grade 9 · Lesson 19
Pythagoras’ Theorem
In any right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides.
a²+b²=c²
Right triangle
Sides a and b meet at a right angle. Side c is the hypotenuse — the longest side, opposite the right angle.
Live triangle
Drag the sliders — watch a, b, and c update. The squares’ areas always satisfy the theorem.
3
4
Live equation
3² + 4² = 5²
9 + 16 = 25
Check: a² + b² = 25 · c² = 25 ✓
Areas side by side
Stack a² and b² — their combined height matches c².
a² + b²
a²
b²
Total 25
c²
c²
Total 25
Try it yourself
Work these without a calculator first — then check.
Question 1 of 3
A right triangle has legs 6 cm and 8 cm. What is the hypotenuse?
Remember
- Only for right-angled triangles.
- c is always the side opposite the right angle.
- To find a leg: a = √(c² − b²).