WARM UPSimplify each radical1.) 2.) 3.)

4.) 5.) 6.)

9.4 SPECIAL RIGHT

TRIANGLES

LEARNING OUTCOMESI will be able to find missing lengths of a

45-45-90 triangle

I will be able to find the missing lengths of a 30-60-90 triangle.

45-45-90 TRIANGLESWhat do we know about the legs of a 45-

45-90 Triangle?

45-45-90 TRIANGLE ACTIVITY1.) Grab a whiteboard and a dry erase marker.

2.) Draw a 45-45-90 triangle in the top right corner of your whiteboard. Give values to the legs (not the hypotenuse) of the triangle. (Use values less than 10)

3.) Leave your board on your desk and stand up.

4.) Go to someone else’s seat and solve for the hypotenuse of the triangle. Leave your answer as a simplified radical.

5.) Switch seats with someone else and double check their work.

45-45-90 TRIANGLE ACTIVITYWhat kind of patterns do you notice?

What will be the hypotenuse of this 45-45-90 triangle?

(Write this down!)

x

x

x

45°

HOW CAN WE USE THIS?Find the hypotenuse of the right triangle.

21

21

21

45°

HOW CAN WE USE THIS?Find the legs of this 45-45-90 Triangle

25

25

25

45°

WHAT ABOUT THESE TYPES OF PROBLEMS?Solve for x

3

x =6 10

= 5

= 5

x

x

45° 45°

YOUR TURN

x = y = 9 x = y =

30-60-90 TRIANGLESAssume this is an equilateral triangle. What is the

height?

2

1

√𝟑

30-60-90 TRIANGLESWhat is the pattern? (WRITE THIS DOWN!)

30°

x2x

x

30-60-90 TRIANGLESFind the missing side lengths based on the given

information.

30°

24

2

30-60-90 TRIANGLESFind the missing side lengths based on the given

information.

30°

510

5

30-60-90 TRIANGLESFind the missing side lengths based on the given

information.

30°

612

6

WHAT ABOUT THESE PROBLEMS?Find the missing values based on the information.

30° 30°

4

9

2

6

3 6

YOUR TURN

x = 14

y = 7

y = 10

x = 5

Draw the triangle and label x and y.

Pg. 554: 12-26, 47-49

EXIT TICKET HOMEWORK