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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