How can you prove a triangle is a right triangle?

Question

rea201 · Answer

As long as one of its angles are 90 degrees it is a right triangle

whpalmer4 · Answer

One way is to see if the sum of the squares of the lengths of the two shortest sides equals the square of the length of the longest side.  The Pythagorean theorem will apply only if it is a right triangle.

kainui · Answer

implying euclidean geometry

anonymous · Answer

Use the Pythagorean theorem a^2+b^2=c^2

whpalmer4 · Answer

@Rea201's suggestion is only helpful if you know the angles, or can exactly determine them.  If you know the lengths of all 3 sides, you can dispense with knowing any of the angles.  A diagram in a test question might not be drawn to scale, for example, so measuring with a protractor could give you the wrong answer, but computing based on the side lengths will give you the true answer.

rea201 · Answer

Or is you now trigonometric function than you can find the angles of the triangles with the sides if you have to know the angles.

whpalmer4 · Answer

Not criticizing it, just pointing out limitations.  And as @kainui points out, the Pythagorean theorem requires Euclidean geometry. (I think that is probably a safe assumption for this question, but the point is valid)

rea201 · Answer

You are right we all have good points. And I didn't take offense to any of. Mathematics has many formulas and different ways to solve different problems. And plus it is a good topic to have a conversation about.