Which of the following triangles are right triangles? Check all that apply

A triangle with side lengths 4, 5, 6

A triangle with side lengths 6 inches, 8 inches, 10 inches

A triangle with side lengths 8, 15, 17

A triangle with side lengths 5, 12, 13

Pythagoras theorem converse : -

if a^2 = b^2 + c^2 then triangle is right angled.

(where a, b and c are measure of the 3 sides and a = hypotenuse (greatest side).

the last one is a right angled triangle because 13^2 = 5^2 + 12^2 (169 = 25 + 144)

There are 2 more Can you find them

does 10^2 = 6^2 + 8^2?

If they are right triangles, they'll satisfy Pythagoras theorem:

a^2 = b^2 + c^2, with the longest side:

No: 6^2 = 4^2 + 5^2

Yes: 10^2 = 6^2 + 8^2

Yes: 17^2=15^2+8^2

Yes: 13^2 = 12^2 + 5^2

All but the first are right triangles. Check the 2nd, 3rd and 4th!