Identifying right-angled triangles using Pythagoras' theorem
It is possible to determine if a triangle contains a right angle using Pythagoras's theorem applies to right-angled triangles. The area of the square drawn on the hypotenuse is equal to the sum of the squares drawn on the other two sides. .
If the squares of the two shorter sides add up to the square of the longest side, the triangle contains a right angle.
Example
Does the triangle ABC contain a right angle?
\(5^2 + 6^2 = 25 + 36 = 61\)
The longest side of the triangle is 8 cm.
\(8^2 = 64\)
61 does not equal 64. Therefore, the triangle does not contain a right angle.
Question
Does the triangle PQR contain a right angle?
\(5^2 + 12^2 = 25 + 144 = 169\)
The longest side of the triangle is 13 cm.
\(13^2 = 169\)
Therefore, the triangle does contain a right angle.