Pythagoras’ theorem · Grade 8

In Grade 8 you learn: Pythagoras’ theorem and finding a shorter side.

In a right-angled triangle, the square on the longest side (the hypotenuse, opposite the right angle) equals the sum of the squares on the other two sides. Pythagoras’ theorem finds a missing side, a distance between points, or checks whether a triangle has a right angle.

Key facts

• a² + b² = c², where c is the hypotenuse.
• Finding the hypotenuse: add the squares, then square root.
• Finding a shorter side: subtract the squares (c² − a²), then square root.
• Distance between two points: √((change in x)² + (change in y)²).
• If a² + b² = c² for the sides, the triangle is right-angled.

Worked examples

Other years

• Pythagoras’ theorem · Grade 9