Testing a Triangle

Part of the Triangles section of Coddy's Geometry journey. Lesson 41 of 71.

You can run the right-angle test by working out one number. Square the two shorter sides and add them. Then subtract the square of the longest side. For sides 6, 8 and 10:

6^2 + 8^2 - 10^2

36 + 64 - 100

A result of zero means the squares of the two shorter sides add up to the square of the longest side, so the triangle is right. Any other result means the triangle is not right.

To test any triangle, first find the longest side. Add the squares of the other two sides, then subtract the square of the longest side. If the result is zero, the triangle is right-angled. If the result is not zero, its sign tells you whether the triangle is acute or obtuse. The next lesson shows how.

Challenge

A triangle has sides 5, 12 and 13. Run the right-triangle test: add the squares of the two shorter sides, then subtract the square of the longest side.

Work the expression out fully.

Try it yourself

5^2 + 12^2 - 13^2

Simplify the expression

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Testing a Triangle

All lessons in Triangles