Discovering Geometry
§9.1-9.4 Worksheet
Name
(ANSWERS W/ WORK ON WEBSITE)
Complete problems 1-5 on page 498 of your textbook here.
1.
2.
3.
4.
5.
Find the value(s) of indicated variable(s). Show all work and simplify all radicals.
1.
2.
x
21
2
75
x
x
3.
4.
6
x
26
24
3
1. No, only about 33.5 inches
1.
x 72
2.
x
2 2
2. 10 meters
3.
x 20
3. 50 km/h
4. x
3 3
4. 8 feet
5. Area: 60 m2, cost $7200
5.
6.
6
8 3
x
12
x
3
Decide whether the set of numbers can represent the side lengths of a triangle. If
they can, classify it (acute, obtuse, or right) Refer to your book on p. 480 if you need help.
7.
14, 48, 50
8.
75, 85, 50
9.
A picket fence is to have a gate 42 inches wide. The gate is 54 inches high. Find
the length of a diagonal brace for the gate to the nearest inch.
10.
A sailboat on Lake Michigan sails 3 miles due north, 4 miles due east and then 5
miles due south. To the nearest tenth of a mile, how far is the boat from its
starting point?
Use the converse of the Pythagorean Theorem to determine whether each triangle is
a right triangle.
11.
12.
6
12
6. x 3 5
13. yes
13.
15
8
6
36
6 5
5. x 4 3
12. No acute
4 95
7. Right
8. Acute
9. 68 inches
10. 4.5 miles
10
11. yes
Use the 30-60-90 and 45-45-90 Conjectures to find all missing lengths.
14.
15.
16.
12
3 2
4
17.
18.
19.
24
7 3
60º
60º
9
20.
60º
21.
22.
60º
60º
12 3
5
12
23.
24.
25.
8
9
60º
7
60º
26.
27.
10
28.
60º
15
2 3
14. 4, 4 2
15. 3, 3
20. 12,12 2
21.
25. 3.5,3.5 3
16. 6 2, 6 2
5 3 10 3
,
3
3
26. 10,10 2 27. 5 3,10 3
17. 18,9 3
18. 7, 14
19. 12,12 3
22. 18,6 3
23. 6 3,3 3
24. 4 2, 4 2
28. 2 3, 2 6
29.
Find the length of a diagonal of a square with sides 10 inches long.
30.
Find the length of a side of a square whose diagonal is 4 cm.
31.
One side of an equilateral triangle measures 6 cm. Find the measure of an
altitude of the triangle.
32.
Find the area of an isosceles triangle with a base of length 20 cm and congruent
sides of length 15 cm.
33.
A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder
is 3 feet from the house. How far above the ground does the ladder touch the house?
Approximate your answers to the nearest tenth.
34.
A baseball field has 90ft between each base. During warm-ups, the third baseman
throws the ball to the second baseman who then throws the ball to the first baseman.
29. 10 2
a)
How far did the ball travel?
b)
During a game the above route is not the one a third baseman would use
to get a runner out at first. Why? Support your answers.
30. 2 2
31. 3 3
32. 50 5
33.
91 or 9.54
34a. 180 feet b.
shorter by 52.7