5.8 Special Right Triangles Day 1: 45-45-90

Part 1: Follow the instructions below for the next three examples.

A. In the given square, draw a diagonal from the lower left corner to the upper right corner. B. Identify and label all angle measures. C. Below the square, redraw the lower right triangle formed in the square. D. Find the missing length of the triangle in simplified radical form.

Example 1: Example 2: Example 3:

Part 2: Drawing conclusions and finding patterns.

E. When a diagonal is drawn in a square, two right triangles are created. What are the three angle measures in each triangle?

F. The hypotenuse of the right triangles you created should have always been a multiple of the legs. What number did the legs get multiplied by to find the hypotenuse?

G. Label the missing sides of the 45˚- 45˚- 90˚triangle to the right.

H. If you know the hypotenuse of a 45˚- 45˚- 90˚triangle, what would you do to calculate the length of the leg?

Summary:

B

A

E

R

3 3

L

O

I

N

5 5

S

A

E

L

8 8

x

x

y

x

9 cm

y

x

3 cm

7 2 m

x

y

x

y1010

y

x

4 2 cm

Directions: For each problem, find the lengths of the other two sides of the triangle.

(Note: Diagrams are not drawn to scale.)

1) 2)

3) 4)

5) 6)

7) A major league baseball diamond is a square with each side measuring 90-ft. How far is it

from home plate to second base, to the nearest hundredth of a foot?

y

x

3 cm12 cm