Honors Geometry Worksheet 5



7.4 Special Right Triangles

Pre-AP Geometry

EVALUATE

I. Find the value of each variable. Write your answer in simplest radical form.

1. 2.

3. x = __________ y = __________ 4. x = __________ y = __________

5. Find the length of the wire

and the height of the pole.

II. True or False: Decide if the statements are true or false. If false, write a corrected statement.

6. Every isosceles triangle is also a right triangle.

7. The diagonal of a square separates it into two isosceles right triangles.

8. The legs of a 45-45-90 right triangle are congruent.

9. The hypotenuse of a 30-60-90 triangle is twice the length of the shorter leg.

10. The hypotenuse of an isosceles right triangle is [pic] times the length of either leg.

11. In a 30-60-90 right triangle the shorter leg is opposite the 60[pic] angle.

III. Make a drawing for each problem and show all work. Leave answers as simplified radicals.

12. Find the perimeter of a square if a diagonal length is 12 feet.

13. The ratio of the legs of a right triangle is 3:1 and the hypotenuse is 10. Find the measure of

each leg.

14. Find the perimeter of an equilateral triangle with an altitude length 7[pic].

IV. Use the parallelogram below to answer the following questions. Leave your answers in simplest radical form when possible. NO decimals used for radicals!

15. Find the measure of angle A in parallelogram 16. Find AD.

ABCD.

17. Find the area of the parallelogram ABCD. 18. Find the perimeter of quadrilateral XBYD.

-----------------------

4

a

12

12 ft

b

10

45(

60(

Ground

4

m

30(

30(

30(

30(

30°

A

NOTE:

In a parallelogram:

- both pairs of opposite sides are congruent and parallel

- both pairs of opposite angles are congruent

- Area = (base)(height)

pole

wire

4.5

B

Name __________________________________

Period _____________ Date ______

45Ú[?]

X

Y

D

C

_

Period _____________ Date ______

45˚

X

Y

D

C

................
................

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