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Geometry Final Exam Review 2nd Semester Name: ______________________________
Unit 3 Part 2
1.
2. Solve for x.
A) B)
3. A 12 ft ladder is leaning against a house. The bottom of the ladder is 7 ft from the base of the house.
Find the angle measure that the ladder makes with the ground? Round to the nearest tenth.
x
50°
8
C
14
A
B
9
x
acute
right
right
obtuse
acute
40
6.7
54.3
4. Solve for x. Round to the nearest tenth.
A) B)
5. Given ∆𝐴𝐵𝐶 is a right triangle with right angle C, find an equivalent ratio for the following:
A) Cos A B) Cos B C) Sin A D) Sin B
For questions 6-7, find the exact missing values.
6. 7.
8. Find the height of the building to the nearest hundredth foot.
9. A 15 ft. ladder is leaning against a shed. The bottom of the ladder is 5.5 ft. from the bottom of the shed.
What is the angle measure to the nearest degree that the ladder makes with the ground? Draw a picture.
10. If the hypotenuse of right triangle ABC is 41 cm with right angle C and sinA=
40
41 find the following:
A) cosA B) tanA
C) sinB D) cosB E) tanB
11 x
29.7° 11
9
x°
29
97 ft
x
x
E
12
T
D
y
6
x
45o
y
12.7
54.9
SinB SinA CosA CosB
x = 24
y = 12√3
x = 3√2
y = 3√2
53.8
68
9
41
40
9
9
41
40
41
9
40
Unit 4: Circles Name the vocabulary term that best describes each arc, point, segment, or line.
1. K ___________________ 2. 𝐶𝐸�̂� ________________
3. 𝐾𝐶̅̅ ̅̅ ___________________ 4. 𝐴𝐶�̂� ________________
5. 𝐴𝐵̅̅ ̅̅ ___________________ 6. 𝐴�̂� ________________
7. 𝑊𝑁̅̅ ̅̅ ̅ __________________ 8. 𝐶𝐷 ⃡ ________________
For questions 9 and 10, use the figure at the right.
9. Name an arc with a measure of 220.
10. Find the measure of 𝐵�̂�.
For questions 11 and 12, use the figure at the right.
11. Find the measure of AB.
12. Find the mDBC.
13. Find the measure of SH. 14. Find the 𝑚∠1.
A
T
E D
C
B
60o
40o
C D
B A
E
60o
45°
A
B C
98°
1
S
H C 38°
K
W
N
C
B A D
E
F
K
Point, center Major arc
radius
diameter
chord
semicircle
Minor arc
Tangent line
arcAED
120
120
45
76
49
72
x
96
15. Solve for x. 16. Find UW
17. The length of a chord of a circle is 19 cm. The chord is 7 cm from the center of the circle. What is the length
of the diameter of the circle?
18. Find the length of one of the tangent segments.
19. Solve for x.
A
B
C
D
E 22
8
120 33
23.6
28.9
9
20. Consider ⨀O, where 𝑚𝐴�̂� = 4𝑥 − 16 and 𝑚𝐵�̂� = 2𝑥 + 22. Find 𝑚∠𝐵𝑂𝐴.
For questions 21 and 22, use the figure at the right.
21. Find the measure of CB.
22. Find the length of DC given AC=4.
23. Solve for x. 24. Solve for x.
25. and are both tangent to the circle. Find the value of x.
AB AC
60 25 x
3
10
x 5
A
B
C
D
30
2 4 x
3030330
0010
D C
B
A
30°
100
150
2.1
110 6
13
26. Find the value of x if mAB = 26° and mCD = 18°.
27. Write an equation of a circle with a center at (2, 13) and a radius of 6.
28. For the equation you wrote above in question 27:
a) Is (1, 4) on the circle? b) Is (2, 7) on the circle?
29. Find the mZ and mY if the mW =82and mX = 108.
30. Find the perimeter of the triangle.
A
B
C
D
O
x
2
5 3
22
(𝑥 − 2)2 + (𝑦 − 13)2 = 36
NO YES
<Z= 72
<Y= 98
20
Find the equation, center and radius for each circle described below:
31. Diameter endpoints (-2, 5) and ( 4, -3). 32. x2 - 12x + y2 + 4 y = 104
33. Center (2,4) contains point (-1, 9) 34. x2 + 4x + y2 – 10y = -28
For #35 – 36, find the exact circumference of each circle
35. 36.
37. Jack uses a compass and a straightedge to construct the perpendicular bisectors of the sides of a triangle.
Describes if the three lines meet inside, outside, on the triangle or do not meet for each triangle:
A) Obtuse triangle B) Acute triangle
38. In the construction, the intersection of the ______________________ of a triangle is the center of the
_____________________ circle.
39. The steps for constructing the inscribed circle of a triangle are shown, but in the wrong order. Put them in
the correct order.
Use the distance from the incenter to point X as the radius, and draw the circle.
Construct the bisectors of two angles of the triangle.
Mark the incenter at the point of intersection
Construct a perpendicular line from the incenter to one side of the triangle. Label this point X.
Step 1: Construct the bisectors of two angles of the triangle
Step 2: Mark the incenter at the point of intersection
Step 3: Construct a perpendicular line from the incenter to one side of the triangle. Label this point X
Step 4: Use the distance from the incenter to point X as the radius, and draw the circle
5
5
12
9
(𝑥 − 1)2 + (𝑦 − 1)2 = 25
C(1,1) r = 5
(𝑥 − 6)2 + (𝑦 + 2)2 = 144
C(6,-2) r = 12
(𝑥 − 2)2 + (𝑦 − 4)2 = 34
C(2,4) r = √34
(𝑥 + 2)2 + (𝑦 − 5)2 = 1
C(-2,5) r = 1
5√2𝜋 15 𝜋
outside
inscribed
Angle bisectors
inside
40. What are the coordinates of the point that 41. Point P lies along the directed line segment
lies 3
8 of the way along the directed line from X(2, -3) to Y(10, 1). Point P partitions the
segment from (-5, 9) to (-1, -7)? segment into a ratio of 3:1. Find the
coordinates of P.
Unit 5: Area, Surface Area, and Volume
1. If mFGH = 135, FG=9 and HG=7, find the area of parallelogram EFGH.
2. If ABCD is a rectangle and CD = 3, BC=6 what is the area of rectangle ABCD?
3. Given the diagonal of square QRST is 14 cm, find the area.
Q
R S
T
(-3.5, 3)
(8, 0)
44.5
18
98
F E
H G
4. Find the area rhombus XWZY.
5. For an exterior angle of 24 in a regular polygon, find the number of sides and the measure of each interior
angle.
6. Given the number of sides of a regular polygon is 9, find the measure of each exterior and interior angle.
7. Determine the area of the shaded sector with central angle of 62° and a radius of 3 cm. Round to the nearest
hundredth.
Convert each angle from radians to degrees or degrees to radians.
8. 37° 9. 150° 10. 4𝜋
3 11.
5𝜋
6
12. Identify the horizontal cross section of the cylinder.
13. What solid would be generated by rotating the figure around the dashed line?
If the sides of the rectangle are 10 cm and 18 cm, what would be the diameter of the base?
4
7
7 cm O
46.0
Int < = 156
15 sides
Ext < = 40
Int < = 140
4.9
37𝜋
180
5𝜋
6
circle
20
240
150
10 ft 4 ft
2 ft
14. In a right triangular prism, describe which polygon would be the cross section made perpendicular to the
base.
15. Find the area of a circle with a diameter of 12.4 yards. Round to the nearest hundredth.
16. Find the surface area and volume. Round to the nearest hundredth.
17. The volume of a rectangular prism is 48,576 𝑐𝑚3. If the height of the prism is 24 cm and the width is 23 cm,
find the length of the prism.
18. Find the surface area and volume. Round to the nearest hundredth.
19. The area of the base of a pyramid is 50ft2 and the height is 6 ft. Find the volume.
20. Find the area of the cross section that is perpendicular to the base and includes the vertex. Find the surface
area and volume. Round to the nearest hundredth.
4 m
9 m
5in
3in
rectangle
120.8
SA=136
V=80
88
SA=326.7
V=452.4
100
12
21. Determine the surface area and volume of a sphere whose diameter is 6 inches. Round to the nearest
hundredth.
22. Determine the surface area and volume of a sphere whose circumference of the great circle is 40𝜋 cm.
23. Find the volume of the hemisphere. Round your answer to the nearest hundredth.
24. Find the volume. Round your answer to the nearest hundredth.
25. Find the surface area and volume. Round your answer to the nearest hundredth.
26. Find the surface area of the prism.
6.2
in.
6 in
6 in
20 in
16 in
10 in
6 in
5 ft
8 ft
6 ft
SA=113.1
V=113.1
SA=5026.5
V=33510.3
V=499.2
V=720
SA=527.8
V=1357.2
SA=152
27. An athletic trainer is using a cylindrical pitcher that is 18 inches tall and has a diameter of 8 inches to fill
a cooler with water. To the nearest tenth, how many pitchers of water will it take to fill the cooler if its
volume is 9,050 cubic inches?
28. If the length of each edge of a rectangular prism is increased by a factor of 8, what factor will the volume
increase by?
29. Did you make your notecard? Do you have pencils and your calculator ready for test day?
Get a good night’s sleep the night before, stretch in the morning, eat breakfast, give yourself plenty of time to
get to school and classes.
GOOD LUCK!!!!!
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