You can understand the Pythagorean Theorem better by looking at two special types of right triangles: the 30-60-90 triangle and the 45-45-90 triangle. Isn't that cool?

30-60-90 Triangle

• The sides of this triangle follow a specific ratio: $1 : \sqrt{3} : 2$.

• This means if one leg of the triangle is $x$, the other leg will be $x \sqrt{3}$, and the longest side (called the hypotenuse) will be $2x$.

• You can see how the Pythagorean Theorem works here. It says $a^2 + b^2 = c^2$, and it fits perfectly with these triangles!

45-45-90 Triangle

• For this triangle, the sides are in a ratio of $1 : 1 : \sqrt{2}$.

• If both legs are the same and equal to $x$, then the hypotenuse will be $x \sqrt{2}$.

• Once again, we can use the Pythagorean Theorem: $a^2 + b^2 = c^2$ works just like it should!

These triangles show us the Pythagorean Theorem in really fun and interesting ways!