Deck 11: Basic Geometry

Question 1

Choose the appropriate sketch for the indicated geometric object.

-Line $\overleftrightarrow{\mathrm{WX}}$

A)
B)
C)
D)

Answer 1

Question 2

Choose the appropriate sketch for the indicated geometric object.

-Line segment $\overline{\mathrm{UV}}$

A)
B)
C)
D)

Answer 2

Question 3

Choose the appropriate sketch for the indicated geometric object.

-Ray $\overrightarrow{\mathrm{WX}}$

A)
B)
C)
D)

Answer 3

Question 4

Choose the appropriate sketch for the indicated geometric object.

-Parallel lines $\overleftrightarrow{\mathrm{PQ}}$ and $\overleftrightarrow{\mathrm{ST}}$

A)
B)
C)
D)

Question 5

Choose the appropriate sketch for the indicated geometric object.

-Perpendicular lines $\overleftrightarrow{\mathrm{AB}}$ and $\overleftrightarrow{\mathrm{CD}}$

A)
B)
C)
D)

Question 6

Choose the appropriate sketch for the indicated geometric object.

-Obtuse angle $\angle \mathrm{DEF}$

A)
B)
C)
D)

Question 7

Choose the appropriate sketch for the indicated geometric object.

-Obtuse angle $\angle \mathrm{TUV}$

A)
B)
C)
D)

Question 8

Choose the appropriate sketch for the indicated geometric object.

-Right angle $\angle X Y Z$

A)

B)

C)
D)

Question 9

Choose the appropriate sketch and description for the indicated geometric object.

-Equilateral $\triangle \mathrm{ABC}$

A) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths; $\angle \mathrm{B}=90^{\circ}$

B) $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}$ are the same length
C) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths
D) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ are the same length

Question 10

Choose the appropriate sketch and description for the indicated geometric object.

-Isosceles $\triangle A B C$

A) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths; $\angle \mathrm{B}=90^{\circ}$

B) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ are the same length
C) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths
D) $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}$ are the same length

Question 11

Choose the appropriate sketch and description for the indicated geometric object.

-Scalene $\triangle A B C$

A) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ are the same length
B) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths

C) $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}$ are the same length
D) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths; $\angle \mathrm{B}=90^{\circ}$

Question 12

Choose the appropriate sketch and description for the indicated geometric object.

-Right $\triangle A B C$

A) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths; $\angle \mathrm{B}=90^{\circ}$

B) $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}$ are the same length
C) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ have different lengths
D) $\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{AC}}$ are the same length

Question 13

Choose the appropriate sketch and description for the indicated geometric object.

-Trapezoid $\overline{R S} \| \overline{T U}$

A) $\overline{\mathrm{RS}}\|\overline{\mathrm{TU}}, \overline{\mathrm{RT}}\| \overline{\mathrm{SU}}$
$\angle \mathrm{R}=\angle \mathrm{S}=\angle \mathrm{T}=\angle \mathrm{U}=90^{\circ}$

B) $\overline{\mathrm{RS}} \| \overline{\mathrm{TU}}$

C) $\overline{\mathrm{RS}}=\overline{\mathrm{TU}}=\overline{\mathrm{RT}}=\overline{\mathrm{SU}}$
$\angle \mathrm{R}=\angle \mathrm{S}=\angle \mathrm{T}=\angle \mathrm{U}=90^{\circ}$

D) $\overline{\mathrm{RS}}\|\overline{\mathrm{TU}}, \overline{\mathrm{RT}}\| \overline{\mathrm{SU}}$
$\overline{\mathrm{RS}}=\overline{\mathrm{TU}}, \overline{\mathrm{RT}}=\overline{\mathrm{SU}}$
$\angle \mathrm{R}=\angle \mathrm{U}, \angle \mathrm{S}=\angle \mathrm{T}$

Question 14

Choose the appropriate sketch and description for the indicated geometric object.

-Circle with center $P$

A)

B)

C)

D)

Question 15

Find the measure of the missing angle(s).

-

A) $67^{\circ}$
B) $113^{\circ}$
C) $46^{\circ}$
D) 23

Question 16

Find the measure of the missing angle(s).

-

A) $118^{\circ}$
B) $28^{\circ}$
C) $152^{\circ}$
D) $62^{\circ}$

Question 17

Find the measure of the missing angle(s).

-
$a=123$ ?

A) $57^{\circ}$
B) $47^{\circ}$
C) $52^{\circ}$
D) $67^{\circ}$

Question 18

Find the measure of the missing angle(s).

-
$\mathrm{a}=42$ ?

A) $138^{\circ}$
B) $133^{\circ}$
C) $128^{\circ}$
D) $148^{\circ}$

Question 19

Find the measure of the missing angle(s).

-
$a=56$ ?

A) $24^{\circ}$
B) $29^{\circ}$
C) $34^{\circ}$
D) $44^{\circ}$

Question 20

Find the measure of the missing angle(s).

-

A) $61^\circ$
B) $71^{\circ}$
C) $81^{\circ}$
D) $66^{\circ}$

Question 21

Find the measure of the missing angle(s).

-

A) $x=132^{\circ} y=48^{\circ}$
B) $x=122^{\circ} y=58^{\circ}$
C) $x=58^{\circ} y=122^{\circ}$
D) $x=32^{\circ} y=148^{\circ}$

Question 22

Find the measure of the missing angle(s).

-

A) $x=109^{\circ} y=71^{\circ}$
B) $x=19^{\circ} y=161^{\circ}$
C) $x=71^{\circ} y=109^{\circ}$
D) $x=119^{\circ} y=61^{\circ}$

Question 23

Find the measure of the missing angle(s).

-
Square

A) $60^{\circ}$
B) $45^{\circ}$
C) $180^{\circ}$
D) $90^{\circ}$

Question 24

Find the measure of the missing angle(s).

-
Parallelogram

A) $\mathrm{A}=124^{\circ}, \mathrm{B}=56^{\circ}$
B) $\mathrm{A}=-34^{\circ}, \mathrm{B}=214^{\circ}$
C) $\mathrm{A}=236^{\circ}, \mathrm{B}=304^{\circ}$
D) $\mathrm{A}=56^{\circ}, \mathrm{B}=124^{\circ}$

Question 25

Find the measure of the requested angle.

-Find the supplement of $40^{\circ}$ .

A) $230^{\circ}$
B) $320^{\circ}$
C) $140^{\circ}$
D) $50^{\circ}$

Question 26

Find the measure of the requested angle.

-Find the supplement of $138^{\circ}$ .

A) Not possible
B) $132^{\circ}$
C) $42^{\circ}$
D) $222^{\circ}$

Question 27

Find the measure of the requested angle.

-Find the complement of $26^{\circ}$ .

A) $64^{\circ}$
B) $244^{\circ}$
C) $154^{\circ}$
D) $334^{\circ}$

Question 28

Find the measure of the requested angle.

-In $\triangle \mathrm{ABC}, \angle \mathrm{A}=57^{\circ}, \angle \mathrm{B}=33^{\circ}$ . Find the measure of $\angle \mathrm{C}$ .

A) $270^{\circ}$
B) $90^{\circ}$
C) $0^{\circ}$
D) $24^{\circ}$

Question 29

Find the measure of the requested angle.

-In parallelogram $A B C D, \angle A=43^{\circ}, \angle B \neq \angle A$ . Find the measure of $\angle B$ .

A) $317^{\circ}$
B) $137^{\circ}$
C) $274^{\circ}$
D) $47^{\circ}$

Question 30

Find the measure of the requested angle.

-In right triangle $A B C, \angle A$ is the right angle, $\angle B=34^{\circ}$ . Find the measure of $\angle C$ .

A) $56^{\circ}$
B) $146^{\circ}$
C) $86^{\circ}$
D) $45^{\circ}$

Question 31

Find the measure of the requested angle.

-In an equilateral triangle, what is the measure of each angle.

A) $60^{\circ}$
B) $30^{\circ}$
C) $90^{\circ}$
D) $45^{\circ}$

Question 32

Solve the problem.

-If a circular pond is $131 \mathrm{ft}$ across, how long a line must a fisherman have to be able to cast to the center of the pond? Round to the nearest hundredth when necessary.

A) $65.5 \mathrm{ft}$
B) $411.34 \mathrm{ft}$
C) $131 \mathrm{ft}$
D) $32.75 \mathrm{ft}$

Question 33

Solve the problem.

-Joe's garden is fenced in and is a square. In the center is a sprinkler that is $57 \mathrm{ft}$ from the front corner. How far is the sprinkler from the back corner? Round to the nearest hundredth when necessary.

A) $28.5 \mathrm{ft}$
B) $57 \mathrm{ft}$
C) $114 \mathrm{ft}$
D) Not enough information to solve

Question 34

Solve the problem.

-A farmer's field is a square $176 \mathrm{yd}$ on each side. What is the radius of the largest crop circle which can be made in the field? Round to the nearest hundredth when necessary.

A) $88 \mathrm{ft}$
B) $352 \mathrm{yd}$
C) $176 \mathrm{yd}$
D) $44 \mathrm{ft}$

Question 35

Solve the problem.

-You wish to make a triangular garden. One of the angles is $42^{\circ}$ . The second angle is complementary to the first angle. What is the measure of the third angle?

A) $90^{\circ}$
B) $96^{\circ}$
C) $48^{\circ}$
D) $45^{\circ}$

Question 36

Solve the problem.

-In a computer game, you are facing a door. If you turn right $70^{\circ}$ , you face a window. The instructions say the angle between the door and the window, plus the angle between the window and the treasure, are supplementary angles. How many degrees more must you turn right to face the treasure?

A) $140^{\circ}$
B) $20^{\circ}$
C) $70^{\circ}$
D) $110^{\circ}$

Question 37

Solve the problem.

-The opening in the top of a recycle bin is in the shape of a trapezoid. The measure of each of the lower angles is $80^{\circ}$ . Find the measure of each of the top angles, which are also equal to each other.

A) $100^{\circ}$
B) $170^{\circ}$
C) $10^{\circ}$
D) $60^{\circ}$

Question 38

Solve the problem.

-A cell phone tower in a city transmits a signal in every direction from the tower. If the coverage area has a radius of 51 miles, what is the diameter of this coverage area?

A) $25.5 \mathrm{mi}$
B) $2601 \mathrm{mi}$
C) $510 \mathrm{mi}$
D) $102 \mathrm{mi}$

Question 39

Find the perimeter or circumference.

-

A) $34 \mathrm{ft}$
B) $33 \mathrm{ft}$
C) $27 \mathrm{ft}$
D) $49 \mathrm{ft}$

Question 40

Find the perimeter or circumference.

-

A) $13.3 \mathrm{~m}$
B) $9.8 \mathrm{~m}$
C) $19.6 \mathrm{~m}$
D) $16.1 \mathrm{~m}$

Question 41

Find the perimeter or circumference.

-

A) $3.7 \mathrm{~m}$
B) $4.7 \mathrm{~m}$
C) $7.4 \mathrm{~m}$
D) $6.4 \mathrm{~m}$

Question 42

Find the perimeter or circumference.

-

A) $78 \mathrm{~m}$
B) $29 \mathrm{~m}$
C) $42 \mathrm{~m}$
D) $299 \mathrm{~m}$

Question 43

Find the perimeter or circumference.

-

A) $276 \mathrm{~m}$
B) $76 \mathrm{~m}$
C) $41 \mathrm{~m}$
D) $29 \mathrm{~m}$

Question 44

Find the perimeter or circumference.

-

A) $16 \mathrm{~cm}$
B) $4 \mathrm{~cm}$
C) $20 \mathrm{~cm}$
D) $10 \mathrm{~cm}$

Question 45

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $37.68 \mathrm{mi}$
B) $113.04 \mathrm{mi}$
C) $18.84 \mathrm{mi}$
D) $75.36 \mathrm{mi}$

Question 46

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $7.379 \mathrm{mi}$
B) $29.516 \mathrm{mi}$
C) $17.341 \mathrm{mi}$
D) $14.758 \mathrm{mi}$

Question 47

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $1017.36 \mathrm{mi}$
B) $113.04 \mathrm{mi}$
C) $226.08 \mathrm{mi}$
D) $56.52 \mathrm{mi}$

Question 48

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $32.970 \mathrm{mi}$
B) $346.185 \mathrm{mi}$
C) $13.335 \mathrm{mi}$
D) $65.94 \mathrm{mi}$

Question 49

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $6.123 \mathrm{mi}$
B) $24.492 \mathrm{mi}$
C) $47.759 \mathrm{mi}$
D) $12.246 \mathrm{mi}$

Question 50

Find the circumference of the circle. Use 3.14 for $\pi$ .

-

A) $270.04 \mathrm{ft}$
B) $67.51 \mathrm{ft}$
C) $5805.86 \mathrm{ft}$
D) $135.02 \mathrm{ft}$

Question 51

Find the perimeter or circumference.

-A rectangle measuring $3 \mathrm{~cm}$ by $12 \mathrm{~cm}$

A) $18 \mathrm{~cm}$
B) $15 \mathrm{~cm}$
C) $12 \mathrm{~cm}$
D) $30 \mathrm{~cm}$

Question 52

Find the perimeter or circumference.

-A square with side $6.7 \mathrm{yd}$

A) $13.4 \mathrm{yd}$
B) $89.78 \mathrm{yd}$
C) $36.8 \mathrm{yd}$
D) $26.8 \mathrm{yd}$

Question 53

Find the perimeter or circumference.

-A square measuring $5.35 \mathrm{~cm}$ on a side.

A) $21.40 \mathrm{~cm}$
B) $10.70 \mathrm{~cm}$
C) $28.62 \mathrm{~cm}$
D) $31.40 \mathrm{~cm}$

Question 54

Find the perimeter or circumference.

-A rectangle measuring $5 \frac{1}{3} \mathrm{~mm}$ by $6 \frac{1}{2} \mathrm{~mm}$

A) $34 \frac{2}{3} \mathrm{~mm}$
B) $11 \frac{5}{6} \mathrm{~mm}$
C) $23 \frac{2}{3} \mathrm{~mm}$
D) $29 \mathrm{~mm}$

Question 55

Find the perimeter or circumference.

-A triangle whose sides measure 10 in., 10 in., and 9 in.

A) 900 in.
B) $50 \mathrm{in.}$
C) 29 in.
D) $\frac{29}{2}$ in.

Question 56

Find the perimeter or circumference.

-A pentagon, five-sided polygon, with equal sides $8 \mathrm{~cm}$

A) $40 \mathrm{~cm}$
B) $320 \mathrm{~cm}$
C) $32 \mathrm{~cm}$
D) Not enough information to solve

Question 57

Find the perimeter or circumference.

-A polygon with sides $11 \mathrm{ft}, 7 \mathrm{ft}, 18 \mathrm{ft}, 22 \mathrm{ft}, 14 \mathrm{ft}$ , and $23.5 \mathrm{ft}$

A) $0.61 \mathrm{ft}$
B) $15.92 \mathrm{ft}$
C) $\frac{191}{4} \mathrm{ft}$
D) $95.5 \mathrm{ft}$

Question 58

Find the perimeter or circumference.

-A circle whose radius measures $12 \mathrm{ft}$ (Use 3.14 for $\pi$ .)

A) $452.16 \mathrm{ft}$
B) $37.68 \mathrm{ft}$
C) $75.36 \mathrm{ft}$
D) $144 \mathrm{ft}$

Question 59

Find the perimeter or circumference.

-A circle whose diameter measures 11 in. (Use 3.14 for $\pi$ .)

A) 69.08 in.
B) $379.94 \mathrm{in.}$
C) $17.27 \mathrm{in}$ .
D) 34.54 in.

Question 60

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $73 \mathrm{ft}$
B) $88 \mathrm{ft}$
C) $78 \mathrm{ft}$
D) $265 \mathrm{ft}$

Question 61

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $54 \mathrm{yd}$
B) $76 \mathrm{yd}$
C) $128 \mathrm{yd}$
D) $72 \mathrm{yd}$

Question 62

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $72 \mathrm{~cm}$
B) $237 \mathrm{~cm}$
C) $57 \mathrm{~cm}$
D) $42 \mathrm{~cm}$

Question 63

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $61.68 \mathrm{~m}$
B) $36.84 \mathrm{~m}$
C) $54.84 \mathrm{~m}$
D) $42.84 \mathrm{~m}$

Question 64

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) 18.42 in.
B) $16.71 \mathrm{in}$ .
C) $13.71 \mathrm{in}$ .
D) $21.42 \mathrm{in}$ .

Question 65

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $132.48 \mathrm{~cm}$
B) $50.24 \mathrm{~cm}$
C) $100.48 \mathrm{~cm}$
D) $164.48 \mathrm{~cm}$

Question 66

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $12.56 \mathrm{ft}$
B) $6.28 \mathrm{ft}$
C) $20.56 \mathrm{ft}$
D) $14.28 \mathrm{ft}$

Question 67

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $31.4 \mathrm{yd}$
B) $82.8 \mathrm{yd}$
C) $61.4 \mathrm{yd}$
D) $47.1 \mathrm{yd}$

Question 68

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $32.84 \mathrm{~m}$
B) $25.84 \mathrm{~m}$
C) $51.68 \mathrm{~m}$
D) $44.68 \mathrm{~m}$

Question 69

Find the perimeter. Use 3.14 for $\pi$ when needed.

-

A) $54.871 \mathrm{~km}$
B) $130.089 \mathrm{~km}$
C) $157.052 \mathrm{~km}$
D) $71.042 \mathrm{~km}$

Question 70

Find the perimeter or circumference. Use $\pi \approx 3.14$ when needed.

-
Round to one decimal place.

A) $63.6 \mathrm{mi}$
B) $56.5 \mathrm{mi}$
C) $14.1 \mathrm{mi}$
D) $28.3 \mathrm{mi}$

Question 71

Find the perimeter or circumference. Use $\pi \approx 3.14$ when needed.

-
Equilateral triangle

A) $312.5 \mathrm{yd}$
B) $74 \mathrm{yd}$
C) $50 \mathrm{yd}$
D) $75 \mathrm{yd}$

Question 72

Find the perimeter or circumference. Use $\pi \approx 3.14$ when needed.

-A circle whose diameter is 3.4 mi long (Round to three decimal places.)

A) $10.676 \mathrm{mi}$
B) $9.075 \mathrm{mi}$
C) $5.338 \mathrm{mi}$
D) $21.352 \mathrm{mi}$

Question 73

Find the perimeter or circumference. Use $\pi \approx 3.14$ when needed.

-A polygon whose side lengths are $5.5 \mathrm{ft}, 4.59 \mathrm{ft}, 2.21 \mathrm{ft}, 6 \mathrm{ft}$ , and $2.9 \mathrm{ft}$

A) $13.64 \mathrm{ft}$
B) $15.8 \mathrm{ft}$
C) $21.2 \mathrm{ft}$
D) $8.24 \mathrm{ft}$

Question 74

Solve the problem.

-A small farm field is a square measuring $280 \mathrm{ft}$ on a side. What is the perimeter of the field? If you double the length of each side of the field, what is the new perimeter?

A) $280 \mathrm{ft}, 1120 \mathrm{ft}$
B) $560 \mathrm{ft}, 2240 \mathrm{ft}$
C) $1120 \mathrm{ft}, 2240 \mathrm{ft}$
D) $560 \mathrm{ft}, 1120 \mathrm{ft}$

Question 75

Solve the problem.

-What will it cost to buy ceiling molding to go around a rectangular room with length $15 \mathrm{ft}$ and width $10 \mathrm{ft}$ ? The molding costs $\$ 2.93$ per linear foot.

A) $\$ 73.25$
B) $\$ 87.90$
C) $\$ 146.50$
D) $\$ 58.60$

Question 76

Solve the problem.

-A pest control company sprays insecticide around the perimeter of a $180 \mathrm{ft}$ by $180 \mathrm{ft}$ building. If the spray costs $\$ 0.11$ per foot, how much did the job cost to the nearest dollar?

A) $\$ 40$
B) $\$ 79$
C) $\$ 297$
D) $\$ 3564$

Question 77

Solve the problem.

-The perimeter of a rectangular room is $52 \mathrm{ft}$ . The width is $9 \mathrm{ft}$ . Find the length.

A) $16 \mathrm{ft}$
B) $18 \mathrm{ft}$
C) $17 \mathrm{ft}$
D) $43 \mathrm{ft}$

Question 78

Solve the problem.

-Mel plans to fence his yard for his new puppy. The yard is a $49 \mathrm{ft}$ by $62 \mathrm{ft}$ rectangle. Fencing costs $\$ 13$ per $10 \mathrm{ft}$ section. What is the cost of the fence not including unused fencing?

A) $\$ 577.20$
B) $\$ 144.30$
C) $\$ 127.40$
D) $\$ 288.60$

Question 79

Solve the problem.

-Tom is going to build a fence around his garden which is a rectangle measuring $8 \mathrm{~m}$ by $20 \mathrm{~m}$ . He will first put in posts which will be $4 \mathrm{~m}$ apart. If the posts cost $\$ 5.50$ each, what will be the total cost for all the posts?

A) $\$ 77.00$
B) $\$ 38.50$
C) $\$ 66.00$
D) $\$ 55.00$

Question 80

Solve the problem.

-A wicker basket has a circular rim with a diameter of $7 \mathrm{in}$ . How many inches of ribbon are needed to go once around the rim? (Use 3.14 for $\pi$ .)

A) 49 in.
B) 19.98 in.
C) 43.96 in.
D) 21.98 in.