Deck 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

Question 1

If X is the midpoint of and X-V-T on , , , , and , find the length of .

Answer 1

29

Question 2

The adjacent angles shown are complementary. If m while m , find an expression for the measure of the right angle in terms of x and y.

Answer 2

Question 3

If m = 34° and m = 46°, then m equals:

Answer 3

80°

Question 4

If m , m , and m = 73°, find x.

Question 5

If (not shown) bisects and m = 37°, then m equals:

Question 6

and intersect at point E. If m and m , find x.

Question 7

If , , and , find x.

Question 8

Let and be a pair of adjacent angles for which m = 37° and m = 49°. If bisects and bisects , find m .

Question 9

If B is the midpoint of and BC = 2.78 inches, then AC measures:

Question 10

Points A, B, and C are collinear. If AB = 12 and BC = 7, find the two possible lengths of .

Question 11

For two intersecting lines, and are a pair of vertical angles formed. Given that m and m , find the value of x.

A) x = 12
B) x = 24
C) x = 36
D) x = 72

Question 12

Complete the following implication with hypothesis "2 + 3 = 5."
If 2 + 3 = 5, then 2a + 3a = ?:

Question 13

If m and m , find m .

Question 14

and are adjacent angles. Where m and m , we have and . Find m .

A) 33°
B) 36°
C) 38°
D) 40°

Question 15

If R-S-T on line RT and while , then ST measures:

Question 16

is separated into smaller angles by and , rays in the interior of .
If m , m , and m , then m equals:

Question 17

Points A, B, C, and D are collinear in the order A-B-C-D. If AC = 10.8 inches,
BD = 7.7 inches, and BC = 3.2 inches, find AD.

Question 18

Suppose that and are complementary. If m and m , find x.

Question 19

and are complementary. Also, m = 38.6° and and are vertical angles.Find m .

Question 20

In the figure, the exterior sides of the adjacent angles ( and ) form a larger angle ( ). If m = 49° and m = 58°, what type of angle is ?

Question 21

If m , m , and m , find x.

A) x = 8
B) x = 8.25
C) x = 8.5
D) x = 8.75

Question 22

Point M is the midpoint of . If AM = 12 and AB = 5x 6, find x:

A) x = 3.6
B) x = 6
C) x = 7.2
D) None of These

Question 23

Points A, B, C, and D are collinear so that A-B-C-D. If AB = 7, AC = 11, and CD = 6, then AD equals:

A) 12
B) 15
C) 17
D) 24

Question 24

If B is the midpoint of line segment AC and AB = 3.6, then AC = 7.2.

Question 25

Where , , and , find .

Question 26

Where and , it follows that .

Question 27

If and are vertical angles with m = 2x 5 and m = 39, then x = 17.

Question 28

A sphere is circumscribed about a cube that has edges of 4 cm. Correct to nearest tenth of a square centimeter, find the approximate surface area for the sphere. Use the calculator value of .

Question 29

Using , find the approximate volume of the sphere with radius 7 inches. Provide result correct to nearest tenth of cubic inch.

Question 30

Given that and , it follows that:

A)
B)
C)
D)

Question 31

What is the exact surface area for a ball with radius 5 inches?

Question 32

For sets R and T, it follows that is the same as:

Question 33

When lines and intersect at point , it follows that .

Question 34

For a given polyhedron, there are 24 vertices and 32 faces. How many edges does the polyhedron have? [Hint: .]

Question 35

For the right circular cylinder, the base has area and the lateral area is . What is the total area of the cylinder?

Question 36

Where P and Q are statements, the compound statement "P or Q" is known as a(n):

Question 37

The surface area of a regular hexahedron is 102 . To the nearest tenth of a centimeter, what is the length of each edge of the hexahedron?

Question 38

Complete the conclusion from the following true statements:
(1) If two triangles are similar, then they have the same shape.
(2) Triangle ABC and triangle DEF are similar.
(C) Triangle ABC and triangle DEF have ? ? ?

Question 39

Given lines and m with , it follows that:

A)
B)
C)
D) None of These

Question 40

If AB = 7.4 and BC = 13.7, then AC = 20.1.

Question 41

A regular icosahedron has its faces numbered 1, 2, 3, . . . , 20 and is used as a die. What is the probability that a roll produces a multiple of 5?

Question 42

Given that each edge measures 4 cm, find the total area of the regular tetrahedron.

A)
B)
C)
D)

Question 43

The volume of a cube is 8 . Find the volume of a cube whose edges are twice those of the first cube.

A) 16
B) 32
C) 48
D) 64

Question 44

The total area for a regular octahedron is . Find the length of each edge of the octahedron.

A) 4 cm
B) 8 cm
C) 12 cm
D) None of These

Question 45

For a box, its height is 4 feet and its volume is 192 . If the length of the rectangular base is 2 feet more than the width of the base, find the width of the base.

A) 6 ft
B) 8 ft
C) 12 ft
D) 16 ft

Question 46

Correct to the nearest tenth of a square foot, find the surface area of a sphere that has a diameter of length 12.8 feet. Use the calculator value of .

A) 257.4
B) 514.7
C) 549.0
D) 1098.1

Question 47

A regular dodecahedron is manufactured as a desk calendar. What is the likelihood that the month facing upward is a month that begins with the letter "J?"

A)
B)
C)
D)

Question 48

Given that 1 foot = 12 inches, how many cubic inches are in one cubic foot?

Question 49

A cube has the volume of 45.6 . Which expression represents the length of each edge of the cube?

A) in
B) in
C) 15.2 in
D) None of These

Question 50

The 8 faces of a regular octahedron are congruent equilateral triangles.

Question 51

The volume of a cube whose sides each measure 1 yard can be written as 9 .

Question 52

What is the name of the geometric figure that is the theoretical limit of an "inscribed" regular polyhedron whose number of faces increases without limit?

Question 53

What is the exact volume for the solid that results when the semicircular region shown is rotated about its diameter of length 6 inches?

Question 54

If the edges of a cube are doubled, then the volume of the new cube will be exactly twice the volume of the original cube.

Question 55

How many edges does a regular octahedron have?

A) 12
B) 10
C) 8
D) 16

Question 56

The volume of a sphere is 564 . Correct to the nearest tenth of a meter, find the length of the radius of the sphere.

A) 6.2 m
B) 5.7 m
C) 5.4 m
D) 5.1 m

Question 57

For the regular dodecahedron with faces numbered 1, 2, 3, . . . , 12, what is the probability that one roll produces a result for 6 or larger? Provide the answer as a common fraction.

Question 58

Find the volume of the box that has dimensions of 10 cm, 12 cm, and 16 cm.

Question 59

In a polyhedron, the relationship between numbers of vertices V, edges E, and faces F is found in Euler's equation .

Question 60

Given that 1 yard = 3 feet, find the number of cubic feet in 1 cubic yard.

A) 27
B) 9
C) 3
D) None of These

Question 61

The total area of a right circular cylinder is . If the height of the cylinder is 4,find the length of the radius.

Question 62

Find the length of slant height l of a right circular cone for which the length of radius is r = 3 cm and the altitude measures h = 4 cm.

Question 63

Where m = 90°, the solid of revolution determined by revolving right triangle about leg is a right circular cone.

Question 64

For a regular square pyramid, each side of the base is 6 inches long. If the altitude of the pyramid measures 9 inches, find the length of each lateral edge correct to the nearest tenth of an inch.

Question 65

A food container is in the shape of a right circular cylinder. To the nearest cubic inch, find the exact volume of the food container if the radius of the base measures 2.3 inches and the height of the container is 6.2 inches.

A) 52
B) 76
C) 92
D) 103

Question 66

One pyramid has a volume of 356 . A larger pyramid has base edges twice as long as that of the first pyramid and a height that is 3 times the height of the first pyramid. What is the volume of the larger pyramid?

Question 67

For a right circular cylinder with radius of base r and length of altitude h, the formula for the lateral area L is:

A)
B)
C)
D) None of These

Question 68

Given that m = 90° and that the triangular region is revolved about side , the related solid of revolution is a right circular cone with radius BC and altitude AC.

Question 69

Use to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

Question 70

A regular square pyramid has base edges of 9 inches and an altitude length of 12 inches. Find the volume of the pyramid.

Question 71

The formula for the volume of a right circular cylinder of radius r and altitude h is given by .

Question 72

A storage tank is in the shape of a right circular cylinder. If r = 3 ft and h = 4 ft,find the exact volume of the cylinder.

Question 73

A right circular cone has a radius of 6 inches and an altitude of 8 inches. Use in order to find the exact total area of the cone.

Question 74

A right circular cylinder of altitude h and with a base of radius r has lateral area L where .

Question 75

A right circular cone has a diameter for its base of length 16 inches and an altitude of 15 inches. Use to find the exact lateral area of the cone.

A)
B)
C)
D) None of These

Question 76

The volume of a right circular cone is exactly . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?

A) 4 ft
B) 4.25 ft
C) 4.5 ft
D) 4.75 ft

Question 77

For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder.

Question 78

The volume V of a sphere with a diameter of length d can be written .

Question 79

For a right circular cone, the altitude has the same measure as its radius. If the volume of the cone is approximately 56 , find the length of radius to the nearest tenth of a foot.

Question 80

A right circular cylinder and a right circular cone with the same circular base and same length of altitude will have the same volume.