GEOMETRY SEMESTER TEST

1275.6 in^3

A cone shaped section is cut out of a cubic block of wood as shown. What is the volume of wood left after the cone is removed? Round to the nearest tenth. #110

y = 1/36x^2

A mirror with a parabolic cross section is used to collect sunlight on a pope located at the focus of the mirror. The pop is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upwards.

144

A road sign is in the shape of a regular decagon. What is the measure of each interior angle on the sign? Round to the nearest tenth.

3,211

A satellite is 6,000 miles from the horizon of Earth. Earths radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earths surface. #82

104.7 cm^3

A solid composed of a right cylinder and a hemisphere is shown. Find the volume to the nearest tenth. #114

<B; DC

A. <H = ? B. GH/DJ = AB/? #28

11.5

AB = 20, BC = 6, and CD = 8 #96

5.4

AB is tangent to circle O and B . Find the length of the radius r for AB = 9 and AO = 10.5. Round to the nearest tenth if necessary. #78

103

ABCD is a parallelogram. If m<CDA = 77, then m<DAB = ? #12

104

ABCD is a parallelogram. If m<DAB = 104, then m<BCD = ? #11

78

AC is tangent to circle O and A. If m arc BY = 24, what if m<YAC? #90

8.4

AD is tangent to circle O and D. Find AB. Round to the nearest tenth if necessary. #94

2.5 cm

Aiden wants to repurpose the wax cylinder shown below by cutting it into 10 equal cylindrical pieces. The cylinder has a radius of 4 cm. How tall is each piece? Round to the nearest tenth. #105

Yes, by AA

Are the two triangles similar? How do you know? #37

Yes, by AA

Are the two triangles similar? How do you know?#36

4.6

Ashanti is supposed to drink 100 oz. of water each day. She bought a refillable cylindrical water bottle to help her. The bottle is 12 in. tall and has a diameter of 2 in. How many bottles of water does Ashanti need to drink? Round to the nearest tenth. (hint: 1 in^3 water = .58 oz water)

45

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. m<O = 135 #79

76

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. m<P = 14 #80

Yes; opposite sides are congruent.

Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. #18

Yes; both pairs of opposite sides are congruent.

Based on the information in the diagram, can you prove that the figure is the parallelogram? Explain. #17

arc AB ~ arc DE

Circle O and P are congruent. What can you conclude from the diagram. # 84

x = 10, DF = 57, EG = 57

DEFG is a rectangle. DF = 6x - 3 and EG = x + 47. Find the value of each diagonal.

Pentagon

Describe the cross section. #99

Cone

Describe the three-dimensional figure that is formed by rotating the right triangle about the line shown? #100

6

Find AM in the parallelogram if PN = 15 and AO = 6. #15

m<1 = 18, m<3 = 72

Find m<1 and m<3 in the kite. #7

31.8 degrees.

Find m<A to the nearest tenth of a degree. #63

30.7

Find the area of a sector with a central angle of 170 degrees and a diameter of 9.1cm. Round to the nearest tenth.

4.84pi

Find the area of the circle. Leave your answer in terms of pi. #77

Center (-6,5); radius 5

Find the center and radius of the circle with equation (x + 6)^2 + (y - 5)^2 =25

36 pi

Find the circumference. Leave your answer in terms of pi. #73

(192pi - 144 square root of 3)

Find the exact area of the shaded region. #75

15 pi

Find the length of arc YPX. Leave your answer in terms of pi. #74

2 square root of 30

Find the length of the altitude drawn to the hypotenuse. #43

8

Find the length of the missing side. #50

Square root of 69 ft

Find the length of the missing side. Leave your answer in simple radical form. #51

20

Find the measure of <BAC in circle O. #89

6

Find the measure of a. #64

172

Find the measure of arc CDE. #72

m<1 = 90, m<2 = 25, and m<3 = 65

Find the measure of the numbered angles in the rhombus. #23

15.26 degrees

Find the missing value to the nearest hundredth. sin ? = 5/19

x = 123, y = 58

Find the missing values of the variables. #5

10,000 pi m^2

Find the surface area of the sphere with the given dimension. Leave your answer in terms of pi. Radius of 50 m.

5 square root of 2 / 2

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form. #53

x = 11 square root 3, y = 22

Find the value of the variables. If your answer is not an integer, leave it in simplest radical form. #54

35.5

Find the value of x for m arc AB = 46 and m and CD = 25. #97

10.7

Find the value of x. If necessary, round to the nearest tenth. #95

11.2

Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. #83

777.9 m

Find the value of x. Round the length to the nearest tenth. #66

6.5 ft

Find the value of x. Round the length to the nearest tenth. #67

57

Find the value of x. Round to the nearest degree. #59

53

Find the value of x. Round to the nearest degree. #60

14.2

Find the value of x. Round to the nearest tenth. #56

5.9

Find the value of x. Round to the nearest tenth. #57

180 cm^3

Find the volume of the composite space figure to the nearest whole number. #104

54 pi in^3

Find the volume of the cylinder in terms of pi. #103

17 m^3

Find the volume of the given prism. Round to the nearest tenth if necessary. #101

215.2 cm^3

Find the volume of the given prism. Round to the nearest tenth if necessary. #102

441 pi in^3

Find the volume of the oblique cone shown in terms of pi. #106

2205.4 m^3

Find the volume of the right cone shown as a decimal rounded to the nearest tenth. #109

2,572 cm^3

Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. #111

605 cm^3

Find the volume of the square pyramid. Round to the nearest tenth if necessary. #107

400 ft^3

Find the volume of the square pyramid. Round to the nearest tenth if necessary. #108

VX/VY = WV/WY

From the similar triangles in the diagram, write a proportion using the ratio WX/WV. #40

284

Given that <DAB and <DCB are right angles and m<BDC = 52 degrees, what is m arc CAD? #88

AP = 10, BP = 15

Given that PQ || BC and AB = 25, what are AP and BP? #47

8 sides

How many sides does a regular polygon have if each exterior angle measures 45?

36

If MJ = 45, KL =48, and ML = 60, what is MK? #41

x = 11, y = 11/3

If ON = 5x - 7, LM = 4x +4, NM = x - 7, and OL = 3y - 7, find the values of x and y for which LMNO must be a parallelogram. #16

300

If m<B = m<D = 30, find m<C so that quadrilateral ABCD is a parallelogram. #19

28 feet

In a diagram of a landscape plan, the scale is 1cm = 10ft. In the diagram, the trees are 2.8 centimeters apart. How far apart should the actual trees be planted.

18 millimeters

In a scale drawing of the solar system, the scale is 1mm = 500km. For a planet with a diameter of 9000 kilometers, what should be the diameter of the drawing of the planet?

x = 15, y = 10

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 2x - 5, and HE = 2y + 5. Find the value of x and y. #14

12

In quadrilateral ABCD, AE = x = 6 and BE = 3x -18. For what value of x is ABCD a rectangle? #27

4

In quadrilateral ABCD, m<ACD = 2x + 4 and m<ACB = 5x - 8. For what value of x is ABCD a rhombus? #25

x = 50, PR = 781, QS = 781

In rectangle PQRS, PR = 16x - 19 and QS = x + 731. Find the value of x and the length of each diagonal. #20

m<2 = 154, m<3 = 13

In the rhombus, m<1 = 154. What are m<2 and m<3? #22

19

In triangle FGH, g = 5, h = 22, and m<F = 50 degrees. Find the measure of f. Round your answer to the nearest whole number.

Isosceles

Is triangle TVS scalene, isosceles, or equilateral? The vertices are T(1, 1), V(9, 2), S(5, 8).

66

JK, KL, and LJ are all tangent to cirlce O, and JK ~ LJ. JA = 9, AL = 10, and CK = 14. Find the perimeter of triangle JKL. #81

34

LM is the midsegment of ABCD. AB = x + 8, LM = 4x +3, and DC = 236. What is the value of x? #10

x = 9, NM = 51, OL = 51

LMNO is a parallelogram. if NM = x + 42 and OL = 5x + 6, find the value of x then find NM and OL. #13

7.2

LO bisects <NLM, LM = 18, NO = 4, and LN = 10. What is the value of x? #48

A triangle ha sides of lengths 27, 79, and 84. Is it a right triangle? Explain.

No; 27^2 + 79^2 does not equal 84^2

56

PQ si tangent to the circle at C. In the circle, m arc AD = 92, and m<D = 78. Find m<DCQ. #91

Parallelogram ABCD is a rhombus, because the diagonal bisects two angles.

Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. #26

Pentagon

Pierre built the model shown in the diagram below for a social studies project. He wants to be able to show the inside of his model, so he sliced the figure as shown. Describe the cross section he created. #98

59 1/6 yards

Plots of land between two roads are laid out according to the boundaries shown. the boundaries between the two roads are parallel. What is the length of Plot 3 along Cheshire Road? #46

Trapezoid

Quadrilateral EFGH has vertices E(-3, 2), F(-1, 6), G(4, 1), and H(1, -2). Which type of quadrilateral best describes EFGH?

5 square root of 2

Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 10 inches long. What is the side length of each piece?

Square

Rebecca wants to demonstrate how you can rotate a two-dimensional polygon to create a cylinder. Which polygon could she use?

ABC ~ MNO; SSS

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. #38

SSS and SAS

Suppose you are given information about a triangle according to SSS, SAS, and ASA. For which of these can you immediately use the Law of Cosines to find on of the remaining measures.

(20.25pi - 40.5)

The area of sector AOB is 20.25pi. Find the exact area of the shaded region #76

63, 117

The isosceles trapezoid is part of an isosceles triangle with a 54 degree vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? #9

x = 9

The polygons are similar, but not necessarily drawn to scale. Find the value of x. #30

x = 13

The polygons are similar, but not necessarily drawn to scale. Find the value of x. #31

2

The polygons are similar, but not necessarily drawn to scale. Find the value of x. #32

24.9

The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth if necessary. #87

308 ft

The students in Mr. Collins class used a surveyors measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. #58

17

The sum of the interior angle measures of a polygon with "s" sides is 2700. Find "s"

91

The sum of the measures of two exterior angles of a triangle is 269. What is the measure of the third exterior angle?

Right scalene

The vertices of triangle JKL are J(-2, 3), K(1, 6), and L(3, -2). Which type of triangle best describes triangle JKL?

7 in

The volume of a cylinder is 980 pi in^3. The height of the cylinder is 20 in. What is the radius of the cylinder?

2.2

To approach the runway, a pilot of a small plane must begin at 10 degrees descent starting fro a height of 1983 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach.#68

Yes, they form a Pythagorean triple; 3^2 + 4^2 = 5^2, and 3, 4, and 5 are all nonzero whole numbers.

Triangle ABC has side lengths 3, 4, and 5. Do the side lengths form a Pythagorean Triple? Explain.

(0, -4)

Triangle ABC is a non right scalene triangle. Two of the vertices are A(-3, -4), and B(2, 1). Which could be the coordinates of point C?

37

Use Euler's Formula to find the missing number. Faces: 20 Vertices: 19 Edges: ?

17

Use Euler's Formula to find the missing number. Vertices: 14 Edges: 29 Faces: ?

13

Use Euler's Formula to find the missing number. Vertices: ? Edges: 36 Faces: 25

43.8

Use the Law of Sines. Find b. #61

85.2 degrees.

Use the Law of Sines. Find m<C to the nearest tenth. #62

48.4

Use the Law of Sines. Find the measure of b, given m<A = 38 degrees, m<B = 74 degrees, and a = 31.

121

Use the diagram. AB is a diameter, and AB is perpendicular to CD. Find m arc BD for m arc AC = 59 #85

80 ft

Use the information in the diagram to determine the height of the tree to the nearest foot. #35

2 km

Viola drives 2 kilometers up a hill that makes an angle of 9 degrees with the horizontal. To the nearest tenth of a kilometer, what horizontal distance has she covered?

211

WZ and XR are diameters. Find the measure of arc ZWX. #86

10 miles

Wayne used the diagram to compute the distance from Ferris, to Dunlap, to Butte. How much shorter is the distance directly from Ferris to Butte that the distance Wayne found#52

(0, -9)

What are the coordinates of the center of a circle with the equation x^2 + (y + 9)^2 =1?

a = 10, b = 2 square root of 26

What are the values of a and b? #42

A' (-3,6), B' (6,3) C' (-6,-6)

What are the vertices of D1.5 #29

D2 x T<0,-6>

What composition of rigid motions and a dilation maps EFGH to the dashed figure. #34

48

What is XZ? #24

y = 1/-4 (x + 4)^2 +1

What is an equation of a parabola with the given vertex and focus? Vertex(-4, 1) focus(-4, 0)

89 degrees

What is m arc EG? #92

3 in

What is the approximate radius of the bowl shown that is shaped as a hemisphere? #113

1437 ft^3

What is the approximate volume of the sphere shown? Round to the nearest tenth. #112

Center (1, -1); radius 2

What is the center and the radius of the circle with the given equation? (x - 1)^2 + (y + 1)^2 = 4

Center (8, 6); radius 7

What is the center and the radius of the circle with the given equation? (x - 8)^2 + (y - 6)^2 = 49

<2 is the angle of elevation from the radar tower to the airplane.

What is the description of <2 as it relates to the situation shows. #65

6 square root of 2

What is the geometric mean of 6 and 12?

4680

What is the sum of the interior angle measures of a 28-gon?

9.3

What is the value of x to the nearest tenth? #49

4 square root of 3

What is the value of y in the right triangle? #44

1072.3 cm^3

What is the volume of a hemisphere with a radius 8 cm? Round to the nearest tenth.

x = 10

What is value of x, given that OP || NQ? #45

JMK ~ MLK ~ JLM

What similarity statement can you write relating the three triangles in the diagram? #39

B ~D and E ~F and A ~C

Which figure are similar? #33

23 units

Which is nearest to the perimeter of WXYZ? #69

The amount of air in a room.

Which situation is best described by surface area? 1. The amount of air in a room. 2. The amount of fabric to make a book cover. 3. The amount of metal to make a soup can. 4. The amount of paint to paint a box.

The amount needed to paint the outside of a can.

Which situation is best described by surface area? 1. The amount of paint a can will hold. 2. The amount needed to paint the outside of a can. 3.The amount of dirt in a cubic planter. 4. The amount of debris stored in a prism shaped landfill.

AA Postulate

Which theorem or postulate proves the two triangles are similar?

(x + 8)^2 + (y + 7)^2 = 4

Write an equation in standard form for the circle. #70

(x - 6)^2 + (y - 5)^2 = 49

Write an equation of a circle with the given center and radius. Center (-6, -5) and radius 7.

(x - 3)^2 + (y - 4)^2 = 16

Write an equation of a circle with the given center and radius. Center (3, 4) and radius 4.

(x + 6)^2 + (y + 8)^2 = 100

Write the standard equation for the circle. center (-6, -8), that passed through (0, 0).

(x + 8)^2 + (y - 6)^2 = 4

Write the standard equation for the circle. center (-8, 6) radius = 2

(x - 3)^2 + (y + 2)^2 = 9

Write the standard equation of he circle in the graph. #71

tan P = 16/12; tan Q = 12/16

Write the tangent ratios for <P and <Q #55

33.5

m arc DE = 120 and m arc BC = 53. Find m<A. #93

20

m<R = 140 and m<S =100. Find m<T. #8