Identifying right-angled triangles using Pythagoras' theorem
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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 hypotenuse, the triangle contains a right angle.
Example
Does the triangle ABC contain a right angle?
\(a^2 + b^2 = c^2\)
\(5^2 + 6^2 = c^2\)
\(61 = c^2\)
The hypotenuse of the triangle is 8.
\(8^2 = 64\)
61 does not equal 64. Therefore, the triangle does not contain a right angle.
Question
Does the triangle PQR contain a right angle?
\(a^2 + b^2 = c^2\)
\(5^2 + 12^2 = c^2\)
\(169 = c^2\)
The hypotenuse of the triangle is 13.
\(13^2 = 169\)
169 is equal to \(c^2\). Therefore, the triangle does contain a right angle.
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