45-45-90 Triangles Lesson

8.2 Special Right Triangles

Math 2

EQ: Wednesday, March 6, 2024

● How do I find the sides of a 45-45-90 Special Right Triangles?

45°

45°

45°−45°−90° = 180o

Multiple Choice

Pythagorean Theorem:

Give the length of the missing side.

• $$2\sqrt[]{5}$$

• 5

• 3

• 10

Multiple Choice

Pythagorean Theorem:

Give the length of the missing side.

• $$2\sqrt[]{5}$$

• 5

• 6

• 7

Multiple Choice

Pythagorean Theorem:

Give the length of the missing side.

• $$\sqrt[]{65}$$

• 11

• 8

• 15

Find the length of the missing side of the right
triangle.

4

7

?

Multiple Choice

Working with Radicals:

Simplify: $$8\times\frac{\sqrt[]{3}}{2}$$

• $$4\sqrt[]{3}$$

• $$8\sqrt[]{3}$$

• $$16\sqrt[]{3}$$

• $$\frac{8\sqrt[]{3}}{16}$$

Multiple Choice

Working with Radicals:

Simplify: $$\frac{2}{3}\times\frac{\sqrt[]{2}}{5}$$

• $$\frac{2\sqrt[]{2}}{15}$$

• $$2\sqrt[]{10}$$

• $$\frac{2\sqrt[]{2}}{8}$$

• $$\frac{2\sqrt[]{5}}{15}$$

Multiple Choice

Working with Radicals:

Simplify: $$\frac{\sqrt[]{3}}{2}\times\frac{\sqrt[]{2}}{3}$$

• $$\frac{\sqrt[]{6}}{6}$$

• $$1$$

• $$\sqrt[]{1}$$

Multiple Choice

Find the measure of angle A.

• 60

• 45

• 90

• 5

Fill in the Blanks

What is the measure of the missing angle θ?

Fill in the Blanks

What is the length of the missing Leg L?

Multiple Choice

What is the length of the missing Hypotenuse H?

• $$5\sqrt[]{2}$$

• $$5$$

• $$4$$

• $$2\sqrt[]{5}$$

Multiple Select

Find the lengths of the missing sides.

• $$L=4$$

• $$H\ =4\sqrt[]{2}$$

• $$L=4\sqrt[]{2}$$

• $$H=4$$

Multiple Select

Find the lengths of the missing sides.

• $$L=9$$

• $$H\ =9\sqrt[]{2}$$

• $$L=9\sqrt[]{2}$$

• $$H=9$$

Multiple Select

Find the lengths of the missing sides.

• $$L=7$$

• $$H\ =7\sqrt[]{2}$$

• $$L=7\sqrt[]{2}$$

• $$H=7$$

Multiple Select

Find the lengths of the missing sides.

• $$L1=7$$

• $$L2\ =7\sqrt[]{2}$$

• $$L1=7\sqrt[]{2}$$

• $$L2=7$$

Multiple Select

Find the lengths of the missing sides.

• $$L1=11$$

• $$L2\ =11\sqrt[]{2}$$

• $$L1=11\sqrt[]{2}$$

• $$L2=11$$

Multiple Select

Find the lengths of the missing sides.

• $$L=\frac{5\sqrt[]{2}}{2}$$

• $$H\ =5$$

• $$L=5$$

• $$H=5\sqrt[]{2}$$

Multiple Select

Find the lengths of the missing sides.

• $$L=\frac{13\sqrt[]{2}}{2}$$

• $$H\ =13$$

• $$L=13\sqrt[]{2}$$

• $$H=13\sqrt[]{2}$$