Question

1. using the patterns seen in problems 1 -6, to fill in the blank spaces of this triangle with hypotenuse x.

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, if the hypotenuse is $x$ and the legs are $a$ and $b$, the ratio of the sides is $a:b:x = 1:1:\sqrt{2}$. So, $a = b=\frac{x}{\sqrt{2}}=\frac{\sqrt{2}x}{2}$.

Answer:

Each of the two legs of the triangle is $\frac{\sqrt{2}x}{2}$