4.3. Special Right Triangles http://www.ck12.org
Confirm with Pythagorean Theorem:
x^2 +(
x√
3
) 2
= ( 2 x)^2
x^2 + 3 x^2 = 4 x^2
4 x^2 = 4 x^2A 45-45-90 right triangle has side ratiosx,x,x
√
2.
Confirm with Pythagorean Theorem:
x^2 +x^2 =(
x√ 2) 2
2 x^2 = 2 x^2Note that the order of the side ratiosx,x√ 3 , 2 xandx,x,x√2 is important because each side ratio has a corresponding
angle. In all triangles, the smallest sides correspond to smallest angles and largest sides always correspond to the
largest angles.
Pythagorean number triples are special right triangles with integer sides. While the angles are not integers, the side
ratios are very useful to know because they show up everywhere. Knowing these number triples also saves a lot of
time from doing the Pythagorean Theorem repeatedly. Here are some examples of Pythagorean number triples: