Geometry Honors: Unit 8 Day 2 Special Right Triangles

Developing the 45-45-90 Triangle ratios !!!!!!!!!!!!!!!!!

!Find the missing side lengths. Answers should be in simplified radical form. !

Learning Target Success Criteria

Section 8-3: Students will be able to use the properties of 45-45-90 triangles and the properties of 30-60-90 triangles.

*I can use the properties of 45-45-90 triangles. !*I can use the properties of 30-60-90 triangles.

If you are given . . . Do thisThe legThe hypotenuse ______________ it by the to get each leg.

�

2______________ it by the to get the hypotenuse.

�

2

1.

! !

3

2.

!

5 2

5. The length of the diagonal of a square is ! . What is the length of a side?

!!!!!!!!!!!Developing the 30-60-90 triangle ratios !!!!!!!!!!!!!!!!!!!!!

3.

!

4. ABCD is a square. Find the length of

! !

�

CB

7 22

!Find the missing side lengths. Answers should be in simplified radical form. !

!

!!!!!!

If you are given. . . Do thisShort leg

Hypotenuse

Long leg

Divide it by 2 to get the short leg. !Then multiply the short leg by to get the long leg.

�

3Divide it by to get the short leg. !Then multiply the short leg by 2 to get the hypotenuse.

�

3

Multiply it by 2 to get the hypotenuse. !Multiply it by to get the long leg.

�

3

6.

!7

30°

7.

!

8

30°

8.

!

2 3

30°

9.

! !5

60°

10.

! !

6

60°

11. A rectangle has a diagonal 20 inches long that forms angles of 60° and 30° with the sides. Find the perimeter of the rectangle. !!!!!12. Triangle ABC is an equilateral triangle with . Find the measure of its altitude. !!!!!!!!Problems Involving More Than One Triangle !Solve for x.

!15. A quilt has the design shown in the figure, in which a square is divided into 8 isosceles right triangles. If the length of one side of the square is 3 inches, what are the dimensions of each triangle? !!!!!!

�

AB =10

13.

! !!

14.

! !!