Question

geo b - 9.2 pythagorean theorem and special cases -lab worksheet
in exercises 1–4, find the value of x. write your answer in simplest form.
1.
2.
3.
4.

Explanation:

Step1: Identify 45-45-90 triangle rules

In a 45-45-90 right triangle, legs are equal, hypotenuse = leg $\times \sqrt{2}$.
---

Problem 1

Step1: Leg = 10, find hypotenuse

Hypotenuse $x = 10\sqrt{2}$
---

Problem 2

Step1: Legs = $\frac{\sqrt{2}}{2}$, find hypotenuse

$x = \frac{\sqrt{2}}{2} \times \sqrt{2}$

Step2: Simplify the expression

$x = \frac{2}{2} = 1$
---

Problem 3

Step1: Hypotenuse = $8\sqrt{2}$, find leg

$x = \frac{8\sqrt{2}}{\sqrt{2}}$

Step2: Simplify the expression

$x = 8$
---

Problem 4

Step1: Hypotenuse = 12, find leg

$x = \frac{12}{\sqrt{2}}$

Step2: Rationalize the denominator

$x = \frac{12\sqrt{2}}{2} = 6\sqrt{2}$

Answer:

1. $\boldsymbol{10\sqrt{2}}$
2. $\boldsymbol{1}$
3. $\boldsymbol{8}$
4. $\boldsymbol{6\sqrt{2}}$