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Unit 2 Pythagorean Theorem Review

Total questions: 125

Worksheet time: 4hrs 30mins

Name
Class
Date
1.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

2.

What side(s) will always be the longest on a right triangle?

a)

The Hypotenuse

b)

Leg A

c)

Leg B

d)

The Right Angle

3.

What side(s) will always be the shortest on a right triangle?


Select all that apply

a)

The Hypotenuse

b)

Leg A

c)

Leg B

d)

The Right Angle

4.
The legs form what type of angle?
a)
Acute
b)
Obtuse
c)
Reflex
d)
Right
5.

What is the relationship between the sides in the Pythagorean Theorem shown?


Hint: Think about when the hypotenuse is missing!

a)

a + b = c

b)

a2 + b2 = c2

c)

a2 – b2 = c2

d)

a – b = c

6.
Do three squares with side lengths of 6, 12, and 13 form a right triangle?
a)
Yes
b)
No
7.
If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?
a)
9
b)
40
c)
41
8.
Do the segment lengths 9, 12, and 15 form a right triangle?
a)
Yes
b)
No
9.
Do these 3 side lengths form a right triangle?
13, 80, and 81?
a)
yes
b)
no
10.

If the sides of a triangle are 7, 24, and 25, is it a right triangle?

a)
yes
b)
no
11.
a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?
a)
yes 
b)
no
12.
Isabella has sticks that are 10cm, 11cm, and 13cm long.  Can she place the sticks together to form a right triangle?  Justify your answer.
a)
No, because 10+11 does not equal 13
b)
No, because 100+121 does not equal 169
c)
Yes, because there is a small side, medium side and long side
d)
Yes, because a triangle has 3 sides
13.

How long is the hypotenuse of this triangle?

(a)  

14.

Is this a right triangle?

a)

Yes

b)

No

15.

Is this a right triangle?

a)

Yes

b)

No

16.

Is this a right triangle?

a)

Yes

b)

No

17.

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

a)

Yes

b)

No

18.

Is a triangle with side lengths of 7, 4, and 4 a right triangle?

a)

Yes

b)

No

19.

Find the missing side.

a)

18

b)

16

c)

17

d)

19

20.

Find the missing side.

a)

11

b)

12

c)

13

d)

14

21.

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

a)

23

b)

26

c)

28

d)

25

22.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
23.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

24.

Which side is the hypotenuse?

a)

9

b)

x

c)

14

25.

Which sides are the legs of the triangle?

a)

9 and 15

b)

9 and 12

c)

12 and 15

d)

15

26.

Which equation can be used to solve for "x"?

a)

152 – x2 = 212

b)

x2 – 152 = 212

c)

152 + 212 = x2

d)

212 – 152 = x2

27.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

28.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
29.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
30.
Find the value of x.
a)
7
b)
8
c)
9
d)
10
31.
solve for c
a)
7
b)
9
c)
4
d)
13
32.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

33.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

a)

180 feet

b)

90 feet

c)

13.4 feet

d)

127.3 feet

34.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

35.

How do you feel about applying and using the Pythagorean theorem?

a)

I am lost

b)

I think I get it

c)

I got it

d)

EASY PEASY

36.

Find the prime factorization of 18

a)

2 • 9

b)

22 • 3

c)

2 • 32

d)

3 • 6

37.

Find the prime factorization of 60

a)

5 • 12

b)

2 • 32 • 5

c)

22 • 3 • 5

d)

27

38.

Find the prime factorization of 30

a)

22 • 5 • 7

b)

2 • 32

c)

2 • 3 • 7

d)

2 • 3 • 5

39.

Find the prime factorization of 81

a)

22 • 7

b)

23 • 5 • 7

c)

43

d)

34

40.

Find the prime factorization of 108

a)

23 * 32

b)

22 • 33

c)

25 • 3

d)

2 • 3 • 7 • 11

41.

Find the prime factorization of 420

a)

22 • 3 • 5 • 7

b)

77

c)

22 • 3 • 11

d)

23 • 3 • 7

42.

What is the greatest common factor of 36 and 40

a)

2

b)

9

c)

4

d)

8

43.

What is the greatest common factor of 60 and 75

a)

2

b)

5

c)

15

d)

25

44.

What is the greatest common factor of 36 and 54

a)

2

b)

6

c)

9

d)

18

45.

What is the greatest common factor of 60 and 84

a)

2

b)

6

c)

12

d)

24

46.

What number has the prime factorization of 23 • 11?

a)

55

b)

66

c)

88

d)

99

47.

What number has the prime factorization of 23 • 32 • 5?

a)

360

b)

720

c)

180

d)

240

48.

Select all of the prime numbers.

a)

1

b)

2

c)

7

d)

18

e)

21

49.

Select all of the prime numbers.

a)

0

b)

19

c)

31

d)

47

e)

51

50.

28 is a _______________ number

a)

prime

b)

composite

51.

If two numbers do not share any common factors, they are considered to be _____________________________.

a)

Prime

b)

Half Prime

c)

Relatively Prime

d)

Sorta Prime

52.

All odd numbers are prime

a)

True

b)

False

53.

All even numbers are composite

a)

True

b)

False

54.

2 is the only even prime number

a)

True

b)

False

55.

The correct way to write prime factorization is _______________________.

a)

greatest to least

b)

least to greatest

c)

alphabetical order

56.
Is 5 prime or composite? 
a)
Prime
b)
Composite
57.
A prime number
a)
has one factor
b)
has more than 2 factors
c)
has 100 factors
d)
has exactly 2 factors: 1 and the number
58.
2 x 2 x 2 is the prime factorization of
a)
6
b)
12
c)
22
d)
8
59.

Use a factor tree to find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

60.

Use a factor tree to find the prime factorization of 32

a)

2x2x2x4

b)

2x2x2x2x2

c)

4x4x2

d)

2x2x2x2x1

61.

Use a factor tree to find the prime factorization of 60

a)

5x3x2x2

b)

7x6x5

c)

5x3x3x2

d)

7x5x4

62.

Use a factor tree to find the prime factorization of 42

a)

4x4x3

b)

6x7

c)

7x3x2

d)

5x4x2

63.

Use a factor tree to find the prime factorization of 64

a)

4x4x4

b)

4x4x2x2

c)

2x2x2x2x2x2

d)

4x4x2x1

64.

Use a factor tree to find the prime factorization of 33

a)

33

b)

11x3

c)

10x3

d)

3x3x3x2

65.

Use a factor tree to find the prime factorization of 72

a)

2x2x2x3x3

b)

4x3x3x2

c)

4x2x2x2x2

66.

52

(a)  

67.

112

(a)  

68.

42

(a)  

69.

1- Which number is a perfect square?

a)

a) 32

b)

b) 25

c)

c) 22

d)

D) 24

70.

3- Which number is perfect square?

a)

a) 36

b)

b) 39

c)

c) 89

d)

d) 11

71.

4- Which number is a perfect square?

a)

a) 100

b)

b) 110

c)

c) 120

d)

d) 59

72.
√16
a)
4
b)
8
c)
2
d)
9
73.
√121
a)
12
b)
10
c)
11
d)
3
74.
√36
a)
4
b)
3
c)
6
d)
5
75.
√256
a)
14
b)
16
c)
13
d)
17
76.
The area of a square is 36 cm2.  What is the length of one side?
a)
6 cm
b)
24 cm
c)
9 cm
d)
9 cm
77.

The area of a square picture frame is 100 cm2.  What is the perimeter of the frame?

a)
25 cm
b)
10 cm
c)
40 cm
d)
50 cm
78.
If I know the area of a square, how do I find the side length?
a)
I square the area.
b)
I divide the area by 2.
c)
I take the square root of the area.
d)
I divide the area by 4.
79.

A perfect square is a number whose square root is ___________.

a)

even

b)

a never-ending

(non-terminating) decimal

c)

rational

d)

odd

80.
To find the square root of a number, you must divide it by 2.
a)
True
b)
False
81.
The √20 is between which two consecutive integers?
a)
2 & 3
b)
3 & 4
c)
4 & 5
d)
5 & 6
82.
Between which two consecutive whole numbers is the√200? 
a)
13 and 14
b)
15 and 16
c)
14 and 15
d)
11 and 12
83.
x² = 121
What does x equal?
a)
11²
b)
11 and -11
c)
20 and 11
d)
12 and 1
84.
What is the square root of 289?
a)
13
b)
140
c)
17
d)
18
85.
What is the square root of 324?
a)
16
b)
17
c)
18
d)
19
86.

Which number has a square root that is between 7 and 8?

a)

48

b)

81

c)

60

d)

36

87.
The number 500...
a)
is a perfect square.
b)
is not a perfect square.
88.

172 =

a)

34

b)

289

c)

225

d)

324

89.

All the following are perfect squares except for which one?

a)
81
b)
121
c)
361
d)
198
90.

The number 125 is...

a)

a perfect square.

b)

not a perfect square.

91.
What is the area of a square with a side of 7?
a)
14
b)
28
c)
49
d)
64
92.
What is the perimeter of a square with a side of 3?
a)
9
b)
12
c)
6
d)
24
93.
If I know the area of a square, how do I find the side length?
a)
I square the area.
b)
I divide the area by 2.
c)
I take the square root of the area.
d)
I divide the area by 4.
94.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

95.
a)
8
b)
9
c)
10
d)
11
96.

364=^3\sqrt{64}=  

a)

-8

b)

8

c)

16

d)

4

97.
Solve for x when x3 = 125
a)
5
b)
10
c)
12
d)
15
98.

92=189^2=18  True or false?

a)

True

b)

False

99.

3216^3\sqrt{216}  

a)

8

b)

9

c)

6

d)

3

100.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

101.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.9 feet

102.

In the Old West, settlers made tents out of a piece of cloth thrown over a clothesline and then secured it to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide?

a)

14.4 feet

b)

7.2 feet

c)

10 feet

d)

20 feet

103.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

a)

180 feet

b)

90 feet

c)

13.4 feet

d)

127.3 feet

104.

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

105.

During a football play, Odell Beckham Jr. runs a straight route 40 yards up the sideline before turning around and catching a pass thrown by Eli Manning. On the opposing team, a defender who started 20 yards across the field from Beckham saw the play setup and ran a slant towards Beckham. What was the distance the defender had to run to get to the spot where Beckham caught the ball?

a)

34.6 yards

b)

44.7 yards

c)

60 yards

d)

40 yards

106.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run?

a)

105 meters

b)

79.4 meters

c)

210 meters

d)

150 meters

107.

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

a)

9 feet

b)

19.2 feet

c)

81 feet

d)

369 feet

108.

The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?

a)

375 in2

b)

70 in2

c)

300 in2

d)

20 in2

109.

Jill's front door is 42" wide and 84" tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door?

a)

Yes

b)

No

110.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

111.

Town A is 90 miles from Town B, and 18 miles from Town C. Town A, B, and C are forming a right triangle at A. A road connects towns B and C directly. Find the length of this road.

a)

108 miles

b)

91.8 miles

c)

88.2 miles

d)

72 miles

112.

Two sides of a right triangle are 8 and 12. Find the missing side length if 8 and 12 are legs.

a)

4.5

b)

20

c)

8.9

d)

14.4

113.

Two sides of a right triangle are 8 and 12. Find the missing side if 8 and 12 are a leg and hypotenuse.

a)

14.4

b)

8.9

c)

20

d)

4.5

114.

Find the area of the missing square off of leg A if the area of one square is 369 and the area of another is 81?

a)

21.2

b)

17

c)

450

d)

288

115.

The three sides of triangle ABC measure 16 meters, 24 meters, and 29 meters. Is triangle ABC an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

116.

The three sides of triangle JKL measure 11.2 meters, 21 meters, and 23.8 meters. Is triangle JKL an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

117.

The three sides of triangle XYZ measure 13 meters, 17 meters, and 21 meters. Is triangle XYZ an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

118.

The three sides of triangle DEF measure 10 meters, 7 meters, and 17 meters. Is triangle DEF an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

119.

The area of a square is 81 square centimeters. Find the length of the diagonal.

a)

9 cm

b)

12.7 cm

c)

18 cm

d)

40.5 cm

120.

Jacob wants to buy a 52” television to fit in his 31 inch by 42 inch opening in his entertainment center. Will the television fit?

a)

yes

b)

no

c)

not sure

121.

Johnathan is painting the side of his home. He has a 25 foot ladder and leans the ladder against his house. The base of the ladder is five feet from the side of the house. How far up the house will the ladder reach?

a)

24 ft

b)

30.2 ft

c)

24.5 ft

d)

25.1ft

122.

Destiny walks out her door and walks due South 150 yards and then turns due East and walks 200 yard to Samantha’s front door. If Jessica wanted to leave Samantha’s home and walk home without making any turns, how far must she walk?

a)

125 yd

b)

62500 yd

c)

350 yd

d)

250 yd

123.

Caroline measured the distance between three cities on a map that happened to form a right triangle. From Shoreview she traveled north 45 miles to Bloomington then she traveled diagonally 75 miles to Richfield. How far is Richfield to Shoreview? Round to the nearest tenth if necessary.

a)

60 miles

b)

30 miles

c)

120 miles

d)

87.5 miles

124.

Carter wants to build a ramp that has a vertical height of 5.25 ft tall and a horizontal length of 25.75 ft. How long is the diagonal part of the ramp? Round to the nearest tenth if necessary.

a)

26.3 ft

b)

27 ft

c)

31 ft

d)

20.5 ft

125.

The course for a local mud race has the shape of a right triangle. The legs consist of a 2 mile obstacle course on foot and a 4 mile swim course. What is the distance of the cycling course? Round to the nearest tenth if necessary.

a)

4.4 miles

b)

4.5 miles

c)

10 miles

d)

6 miles

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