Deck 9: An Introduction to Geometry

Question 1

Name the vertex and the sides of ∠ ABC .

A) B ; AB and BC
B) C ; AB and BC
C) B ;  AB and AC
D) C ; AC and BC

Answer 1

B ; AB and BC

Question 2

Name anlge 3 in three appropiate ways.

A) ∠ CBE ; ∠ EBC ; ∠ B;
B) ∠1;∠ ABD ;∠ DBA
C) ∠3; ∠ CBE ; ∠ EBC
D) ∠ ABD ; ∠ DBA ; ∠ B

Answer 2

∠3; ∠ CBE ; ∠ EBC

Question 3

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .

-acute

A) AGC
B) FGD
C) BGE
D) BGA

Answer 3

AGC

Question 4

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .

-straight

A) AGC
B) FGD
C) BGE
D) BGA

Question 5

Choose the correct word.
Any _____ different points determine exactly one line.

A) two
B) three

Question 6

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .

-obtuse

A) AGC
B) FGD
C) BGE
D) BGA

Question 7

The illustration shows a block that is suspended with two ropes, one of which is horizontal. The weight of the block is $A = 68$ . Which numbered angle in the illustration is acute?

A) 3
B) 2
C) 1

Question 8

Use the protractor to find the measure of ? GQC .

A) $100 ^ { \circ }$
B) $75 ^ { \circ }$
C) $105 ^ { \circ }$
D) $80 ^ { \circ }$

Question 9

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .

-right

A) AGC
B) FGD
C) BGE
D) BGA

Question 10

What can be a name of a plane? 

A) P
B) PQ
C) XYZ
D) MNPQ

Question 11

Find the complement of a  $34 ^ { \circ }$  angle.

A) $146 ^ { \circ }$
B) $214 ^ { \circ }$
C) $326 ^ { \circ }$
D) $56 ^ { \circ }$
E) $124 ^ { \circ }$

Question 12

Which expression(s) is(are) true?
1. A plane as a geometric figure that has position but no length, width, or depth.
2. Points are labeled with capital letters.
3. A line extends infinitely far in both directions, but has no width or depth.
4. Planes are made up of points.
5. A line is a flat surface, extending infinitely far in every direction, that has length and width but no depth.

A) 1, 2, 3, 4
B) 2, 3, 4
C) 1, 2, 4, 5
D) 1, 2

Question 13

Refer to the figure above to find the length of segment $\overline { DA}$

A) 4
B) 3
C) 2
D) 7

Question 14

In the figure below, a = 105. What is the angle of the handle of the lawn mower in relation to the ground?
__________

Question 15

In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $X$ .

A) 166
B) 39
C) 129
D) 78
E) 64

Question 16

Fill in the blanks.
The ________ AB , written as $\overline { A B }$ , is the part of a line that consists of points A and B and all points in between.
A _______ is the part of a line that begins at some point (say, A ) and continues forever in one direction.

A) line segment, line
B) line, ray
C) line, line segment
D) line segment, ray

Question 17

In the figure below, angle $a = 34 ^ { \circ }$ and angle $b = 68 ^ { \circ }$ .
What is the measure of angle x ?

A) 34
B) 40.5
C) 27.5
D) 129.5
E) none of these

Question 18

Refer to the figure above. Name the midpoint of the segment $\overline { G C}$ . Find a segment, congruent to $\overline { G C}$ .

A) $E$ ; $\overline { A E }$
B) $E$ ; $\overline { B D}$
C) $C$ ; $\overline { A E }$
D) $C$ ; $\overline { B D}$

Question 19

What is a proper name for an angle?

A) BC
B) A
C) PQ

Question 20

In the figure below, $a = 51$ . How many degrees from the horizontal position are the wings of the airplane?

A) 129
B) 51
C) 39
D) 84
E) 309

Question 21

In the figure below, $$a = 128$$ . Find x and y .

A) $x = 52$ , $y = 128$
B) $x = 128$ , $y = 128$
C) $x = 128$ , $y = 52$

Question 22

In the figure below, choose the pair of corresponding angles.

A) $\angle 5$ and $\angle 6$
B) $\angle 1$  and $\angle 6$
C) $\angle 1$  and $\angle 5$
D) all of these
E) none of these

Question 23

Find $\angle 2$ if  $$\angle 1 = 53 ^ { \circ }$$ .

A) $127 ^ { \circ }$
B) $54 ^ { \circ }$
C) $37 ^ { \circ }$
D) $74 ^ { \circ }$
E) $53 ^ { \circ }$

Question 24

Find $\angle 2$  if  $$\angle 1 = 39 ^ { \circ }$$

A) $51 ^ { \circ }$
B) $39 ^ { \circ }$
C) $52 ^ { \circ }$
D) $40 ^ { \circ }$
E) none of these

Question 25

In the figure below, $a = 10$ , $b = 5$ , and  $c = 45$ .
What is the measure of angle y ?

A) 99
B) 189
C) 90
D) 9
E) none of these

Question 26

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 51.08 ^ { \circ }$  and $m ( \angle B ) = 56.46 ^ { \circ }$ .

A) $71.46 ^ { \circ }$
B) $72.46 ^ { \circ }$
C) $82.47 ^ { \circ }$
D) $72.57 ^ { \circ }$
E) $72.36 ^ { \circ }$

Question 27

A triangle with three sides of equal length is called a(n) __________ triangle.

Question 28

An __________ triangle has two sides of equal length .

Question 29

Using the figure below, find $\angle 8$  if $l _ { 1 }$ is parallel to $l _ { 2 }$ with $\angle 2 = 18 ^ { \circ }$ .

A) $161 ^ { \circ }$
B) $162 ^ { \circ }$
C) $71 ^ { \circ }$
D) $18 ^ { \circ }$
E) none of these

Question 30

Find the supplement of a  $46 ^ { \circ }$  angle.

A) $136 ^ { \circ }$
B) $134 ^ { \circ }$
C) $46 ^ { \circ }$
D) $44 ^ { \circ }$
E) $314 ^ { \circ }$

Question 31

In the figure below, $l _ { 1 }$  is parallel with  $l _ { 2 }$ .
Find x , if $a = 6$ , $b = 10$ , $c = 4$  and $$d = - 10$$ .

A) $162 ^ { \circ }$
B) $342 ^ { \circ }$
C) $252 ^ { \circ }$
D) $18 ^ { \circ }$
E) none of these

Question 32

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 113 ^ { \circ }$  and $m ( \angle B ) = 33 ^ { \circ }$ .

A) $34 ^ { \circ }$
B) $44 ^ { \circ }$
C) $33 ^ { \circ }$
D) $214 ^ { \circ }$
E) none of these

Question 33

How many pairs of corresponding angles are shown in the figure below?
__________ pairs of corresponding angles

Question 34

What are two lines which intersect and form right angles called?

A) perpendicular
B) straight
C) intersecting
D) parallel
E) none of these

Question 35

What are two lines in the same plane called?

A) perpendicular
B) intersecting
C) transversal
D) coplanar
E) parallel

Question 36

In the figure below, $l _ { 1 }$ is parallel with  $l _ { 2 }$  and $l _ { 2 }$ is parallel with  $l _ { 3 }$ . What can you conclude about $l _ { 3 }$  and $l _ { 1 }$ ?
They are __________.

A) perpendicular
B) coplanar
C) parallel
D) none of these
E) all of these

Question 37

What is a triangle with three angles of equal measure called?

A) right
B) scalene
C) equilateral
D) isosceles
E) none of these

Question 38

In the figure below, $l _ { 1 }$  is parallel with $l _ { 2 }$ .
Find x , if $a = 5$ , $$b = 4$$  and $$c = 17$$ .

A) $292 ^ { \circ }$
B) $17 ^ { \circ }$
C) $146 ^ { \circ }$
D) $163 ^ { \circ }$
E) none of these

Question 39

Refer to the figure. Which of the following choices are interior angles?

A) ∠8
B) ∠6
C) ∠7
D) ∠5
E) none of these

Question 40

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

A) 25
B) 20
C) 19
D) 24
E) 18

Question 41

The tree in the illustration casts a shadow $c = 6$  feet long, while a person $a = 6$  feet tall casts a shadow $b = 4$  feet long. 
Find the height of the tree.

A) $\frac { 3 } { 12 }$
B) 15
C) $\frac { 1 } { 9 }$
D) 9
E) none of these

Question 42

Refer to the illustration. Find $b$  if $a = 8$  and $c = 10$ .

A) 2
B) $\sqrt { 18 }$
C) $\sqrt { 10 }$
D) 6
E) $\sqrt { 514 }$

Question 43

Below are the lengths of the sides of a triangle. Which is a right triangle?

A) 9, 8, 6
B) 9, 8, 7
C) 6, 8, 10
D) 10, 8, 7
E) none of these

Question 44

The lengths of the sides of different triangles are given below. Which is a right triangle?

A) 5, 12, 12
B) 9, 7, 10
C) 6, 13, 14
D) 5, 12, 13
E) 9, 7, 11

Question 45

Estimate the area of the sail on the windsurfing board.
__________

Question 46

Find the area of the shaded part of the figure if $a = 18$ , $$b = 5$$ .

A) 90
B) 180
C) 45
D) 14
E) none of these

Question 47

In isosceles triangle RST , $\overline { R S } \cong \overline { S T }$ . If $R S = 2 x + 3$ , $R T = x$ , and the perimeter of $\triangle R S T$ is 36, find the value of x .

A) $x = 5.5$
B) $x = 6$
C) $x = 6.5$
D) None of These

Question 48

Find the area of the shaded part of the figure if $$a = 4$$ , $$b = 6$$ .

A) 48
B) 96
C) 12
D) 10
E) none of these

Question 49

Find the missing side lengths in each triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

A) $x = 4 , h = 5$
B) $x = 5 , h = 5 \sqrt { 2 } \approx 5.66$
C) $x = 4 \sqrt { 2 } \approx 5.66 , h = 4$
D) $x = 4 , h = 4 \sqrt { 2 } \approx 5.71$
E) $x = 4 , h = 4 \sqrt { 2 } \approx 5.66$

Question 50

The angles of the triangles shown in the illustration are  $a = 60 ^ { \circ }$ , $b = 60 ^ { \circ }$ . The triangles are congruent because of what property?

A) SAS property
B) ASA property
C) SSS property

Question 51

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

A) $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$
B) $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$
C) $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$
D) $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$
E) $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$

Question 52

FIGURE 1
The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if ft and ft.
c = __________ ft

Question 53

What size is the television screen shown in the illustration? Find d if in. and in.. Please round the answer to the nearest tenth.
__________ in.

Question 54

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $$c = 80$$ .

A) 64
B) 80
C) $\frac { 1 } { 27 }$
D) $\frac { 36 } { 5 }$
E) none of these

Question 55

Are the two triangles shown in the illustration congruent if $a = 48$ ? Why?

A) yes, SAS
B) yes, ASA
C) yes, AAA
D) yes, SSS
E) no

Question 56

Refer to the illustration. Find $C$  if $a = 4$  and $b = 3$ .

A) 5
B) $\sqrt { 60 }$
C) $\sqrt { 18 }$
D) $\sqrt { 17 }$
E) 7

Question 57

The triangles shown in the illustration are congruent. The sides of the triangles are $a = 3$ , $b = 13$ , and $c = 3$ .
So $d = 14$ .

Question 58

A man places a mirror on the ground and sees the reflection of the top of a building, as shown in the illustration. $b = 36$ , $c = 252$ , and $h = 28$ .

A) 32
B) $\frac { 1 } { 6 }$
C) $\frac { 578 } { 3 }$
D) 4
E) none of these

Question 59

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

A) $x = 24$
B) $x = 32$
C) $x = 46$
D) $x = 58$

Question 60

The lengths of the three sides of a triangle are given. The triangle is a right triangle. $a = 9$ , $b = 39$ , $c = 40$

Question 62

Refer to the rectangle ABCD , shown below, where $m ( \angle 4 ) = 18 ^ { \circ }$ .

A) $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$
B) $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$
C) $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$
D) $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$

Question 66

Find the volume of a cone with a height of 10 centimeters and a circular base with a diameter of 9 centimeters.

A) $212.06 \mathrm {~cm} ^ { 3 }$
B) $3,316.81 \mathrm {~cm} ^ { 3 }$
C) $282.74 \mathrm {~cm} ^ { 3 }$
D) $424.12 \mathrm {~cm} ^ { 3 }$
E) $848.23 \mathrm {~cm} ^ { 3 }$

Question 67

Find the total area of the shaded figure.
The diameters of the smaller circles are equal to 8. Use $\pi = 3.1416$ .

A) 150.8
B) 100.5
C) 301.6
D) 175.9
E) none of these

Question 68

Choose case when the triangles are similar.

A) $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$
B) $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$
C) $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$
D) $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$

Question 69

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$  Find its length.

A) $\text { length } = 110 \mathrm {~cm}$
B) $\text { length } = 23 \mathrm {~cm}$
C) $\text { length } = 27 \mathrm {~cm}$
D) $\text { length } = 23.5 \mathrm {~cm}$
E) $\text { length } = 20 \mathrm {~cm}$

Question 70

Refer the trapezoid KLMN below, with $\overline { K L } \| \overline { N M}$ . Find   x and y .

A) $x = 83 ^ { \circ }$ , $y = 57 ^ { \circ }$
B) $x = 53 ^ { \circ }$ , $y = 87 ^ { \circ }$
C) $x = 57 ^ { \circ }$ , $y = 83 ^ { \circ }$
D) $x = 87 ^ { \circ }$ , $y = 53 ^ { \circ }$

Question 71

Classify the following polygons:
1.
2.
3.
4.
5.

A) Picture 1: octagon; picture 2: hexagon; picture 3: quadrilateral; picture 4: triangle and picture 5: pentagon.
B) Picture 1: quadrilateral; picture 2: octagon; picture 3: hexagon; picture 4: triangle and picture 5: pentagon.
C) Picture 1: quadrilateral; picture 2: hexagon; picture 3: octagon; picture 4: triangle and picture 5: pentagon.
D) Picture 1: quadrilateral; picture 2: pentagon; picture 3: octagon; picture 4: triangle and picture 5: hexagon.
E) Picture 1: quadrilateral; picture 2: triangle; picture 3: octagon; picture 4: hexagon and picture 5: pentagon.

Question 72

Suppose that the length of a radius of a circle is the same as the length of a side of a square. If the circumference of the circle is 15.96 centimeters longer than the perimeter of the square, find the length of a radius of the circle. (Use 3.14 as an approximation for π .)

A) 9.28 centimeters
B) 7 centimeters
C) 6.75 centimeters
D) 7.25 centimeters
E) 2.28 centimeters

Question 73

Refer to trapezoid MNOP show below. Find x .

A) 134°
B) 46°
C) 90°
D) 146°

Question 74

Find the volume of a prism whose base is a right triangle with legs 10 and 2 meters long and whose height is 7 meters.

A) $70 \mathrm {~m} ^ { 3 }$
B) $140 \mathrm {~m} ^ { 3 }$
C) $20 \mathrm {~m} ^ { 3 }$
D) $280 \mathrm {~m} ^ { 3 }$
E) $199 \mathrm {~m} ^ { 3 }$

Question 75

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.

A) $324 \mathrm {~m} ^ { 3 }$
B) $108 \mathrm {~m} ^ { 3 }$
C) $973 \mathrm {~m} ^ { 3 }$
D) $1,296 \mathrm {~m} ^ { 3 }$
E) none of these

Question 76

In the figure below, $A B \| C D$ . Are $\triangle A O B$  and $$\triangle C O D$$  similar triangles?

A) Yes
B) No

Question 77

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?

A) 9
B) 8
C) 10
D) 11
E) none of these

Question 78

Find the area of the shaded part of the figure if $a = 6$ , $b = 7$ , $$c = 4$$

A) 49
B) 24
C) 108
D) 66
E) none of these

Question 79

The angle a shown in the illustration is $30 ^ { \circ }$ Find b , if the two triangles are similar.

A) $15 ^ { \circ }$
B) $60 ^ { \circ }$
C) $30 ^ { \circ }$
D) $16 ^ { \circ }$
E) none of these

Question 80

Refer the trapezoid shown below. Find x .

A) 42°
B) 138°
C) 142°
D) 125°