What is the relationship between the size of an angle in a triangle and the length of the sides of the triangle?
If you consider the sum of the squares built on two sides of a triangle (two sides that define an angle) and the square on the third side (the side opposite the angle) you can find a way to determine if an angle is acute, right, or obtuse. Use the sliders in the dynamic worksheet below to explore the relationship between these quantities and the angle between the sides.Goal: State the relationship you have found in your own words.

Consider the sum of the areas of the squares built on the sides of the triangle that bound an angle and the area of the squre built on the side opposite the angle.

For what angles are these things equal?

For what angles does the sum of the squares exceed the square of the third side?

For what angles does the sum of the squares fall short of the square of the third side?

Follow up by viewing this idea applied to specific triangles: