Pythagorean Theorem

Scalene, isosceles, equilateral, acute, right, obtuse.

Yes, the base and height can be congruent.

No, if all three sides were the same length, the triangle would only have 60° angles.

Base, height, and hypotenuse (it’s okay if students don’t name the “hypotenuse” yet).

It depends on your point of view. The base is generally the bottom and the height is at a right angle to it, but the triangle can be rotated so that the side names are swapped.

When I know two side lengths in a right triangle, and I want to calculate the missing side length.

a²=a⋅a, whereas 2a=a+a. For example, 3²=9 and 3×2=6.

Substitute these values into the Pythagorean Theorem to get 6²+8²=c². Simplify to 100=c², and then take the square root to get 10 units.

I can still substitute 6 for a, but now I substitute 8 for c instead of b. The formula 6²+b²=8² yields 36+b²=64, or b²=28. The exact value is square root of 28, which is about 5.3 units, rounded to the nearest tenth.

I draw a triangle with the hypotenuse along the diagonal line that I want to measure. I count the lengths of the legs and substitute them for a and b in the Pythagorean Theorem. Then I can solve for c to find its length.