Converse of Pythagoras’ theorem

Key Notes :

If a2 + b2 = c2, then the triangle is a right triangle. This is called the converse of Pythagoras’ theorem.

Learn with an example

A triangle has sides with lengths of 6 metres, 8 metres, and 13 metres. Is it a right triangle?

  • yes
  • no

Plug in 6, 8, and 13. Use the smaller numbers for a and b and the largest number for c.

a2 + b2 = c2

62 + 82 = 132

36 + 64 = 169

100 ≠ 169

The result is false. So, it is not a right triangle.

A triangle has sides with lengths of 5 kilometres, 12 kilometres, and 13 kilometres. Is it a right triangle?

  • yes
  • no

Plug in 5, 12, and 13. Use the smaller numbers for a and b and the largest number for c.

a2 + b2 = c2

52 + 122 = 132

25 + 144 = 169

169 = 169

The result is true. So, it is a right triangle.

A triangle has sides with lengths of 9 metres, 10 metres, and 12 metres. Is it a right triangle?

  • yes
  • no

Plug in 9, 10, and 12. Use the smaller numbers for a and b and the largest number for c.

a2 + b2 = c2

92 + 102 = 122

81 + 100 = 144

181 ≠ 169

The result is false. So, it is not a right triangle.

let’s practice!