Free Printable Unit 5: Pythagorean Theorem

1.

The legs of a right triangle are represented by a and b, and the hypotenuse of the right triangle is represented by c. Which equation represents the Pythagorean Theorem?

a)

a² + b² = c²

b)

a²+ c²= b²

c)

a + b = c

2.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

3.

Sides a and b are called legs.

a)

true

b)

false

4.

What is the name for side c?

a)

head

b)

body

c)

hippopotamus

d)

hypotenuse

5.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

6.

If the sides of a right triangle are 40, 50, and 30, which sides are the legs?

a)

40 and 50

b)

50 and 30

c)

40 and 30

d)

30, 40, and 50

7.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

8.

What is the area of the third square?

a)

6.7 cm²

b)

33.5 cm²

c)

2025 cm²

d)

45 cm²

9.

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

a)

12 in²

b)

144 in²

c)

194 in²

d)

13.9 in²

10.

If 231 square feet of paint was used to paint the two squares blue, how much paint would be needed to paint the white square purple?

a)

15.2 ft²

b)

115.5 ft²

c)

231 ft²

d)

10.7 ft²

11.

If a = 5 and b = 7, what is the area of square c?

a)

74

b)

8.6

c)

12

d)

6241

12.

Which of the following sentences would belong in the proof that describes this image?

a)

The sum of the areas of the two smaller squares is equal to the area of the large square.

b)

The sum of the side lengths of the two smaller squares is equal to the side length of the large square.

c)

The difference of the areas of the two smaller squares is equal to the area of the large square.

d)

The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

13.

What is the name of your math teacher?

a)

Ms. Garza

b)

Ms. Espinoza

c)

Ms. Garcia

d)

Don't know her

14.

The total sum of areas a and b is equal to the area of c

a)

True

b)

False

15.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

16.

a)

The sum of the areas of Square N and Square L is equal to the area of Square K.

b)

The sum of the areas of Square N and Square L is greater than the area of Square K.

c)

The sum of the areas of Square N and Square K is equal to the area of Square L.

d)

The sum of the areas of Square N and Square K is less than the area of Square L.

17.

a)

F

b)

G

c)

H

d)

J

18.

a)

The number of tiles needed to cover Region X is the same as the number of tiles needed to cover both Region Y and Region Z.

b)

The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region X and Region Z.

c)

The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region X ad Regions Y.

d)

None of these.

19.

The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true?

a)

The sum of the areas of Square A and Square C is equal to the area of Square B.

b)

The sum of the areas of Square B and Square C is greater than to the area of Square A.

c)

The sum of the areas of Square A and Square B is equal to the area of Square C.

d)

The sum of the areas of Square A and Square C is less than to the area of Square B.

20.

The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true?

a)

The sum of the areas of Square A and Square C is equal to the area of Square B.

b)

The sum of the areas of Square B and Square C is less than to the area of Square A.

c)

The sum of the areas of Square A and Square C is greater than to the area of Square B.

d)

The sum of the areas of Square B and Square C is equal to the area of Square A.

21.

The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true?

a)

The sum of the areas of Square blue and Square green is equal to the area of Square red.

b)

The sum of the areas of Square blue and Square red is equal to the area of Square green.

c)

The sum of the areas of Square green and Square red is less than to the area of Square blue.

d)

The sum of the areas of Square blue and Square red is greater than to the area of Square green.

22.

An artist joined three square regions at their vertices to create the figure shown in the diagram. The artist will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

a)

The number of tiles needed to cover Region X is the same as the number of tiles needed to cover both Region Y and Region Z.

b)

The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region X and Region Z.

c)

The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region X and Region Y.

d)

None of these

23.

An artist joined three square regions at their vertices to create the figure shown in the diagram. The artist will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

a)

The number of tiles needed to cover Region blue is the same as the number of tiles needed to cover both Region red and Region green.

b)

The number of tiles needed to cover Region green is the same as the number of tiles needed to cover both Region red and Region blue.

c)

The number of tiles needed to cover Region red is the same as the number of tiles needed to cover both Region blue and Region green.

d)

None of these

24.

An artist joined three square regions at their vertices to create the figure shown in the diagram. The artist will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

a)

None of these

b)

The number of tiles needed to cover Region red is the same as the number of tiles needed to cover both Region purple and Region blue.

c)

The number of tiles needed to cover Region blue is the same as the number of tiles needed to cover both Region purple and Region red.

d)

The number of tiles needed to cover Region purple is the same as the number of tiles needed to cover both Region red and Region blue.

25.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Which three squares do NOT support this statement?

a)

F

b)

G

c)

H

d)

J

26.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Which three squares does support this statement?

a)

A

b)

B

c)

C

d)

D

27.

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Which three squares does support this statement?

a)

F

b)

G

c)

H

d)

J

28.

All of the a square plus all of the b square will perfectly fill the c square with nothing left over.

a)

True

b)

False

29.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

30.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

31.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

32.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

33.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

34.

Find the distance.

a)

7.1

b)

7.8

c)

8.7

d)

8.9

35.

Find the distance between the two points.

a)

7.3 units

b)

8.1 units

c)

7.7 units

d)

9.1 units

36.

What is the diagonal distance between the two points?

a)

10.2 units

b)

9.9 units

c)

9.3 units

d)

8.7 units

37.

Find the distance between the two points.

a)

2.2 units

b)

3.5 units

c)

4.1 units

d)

2.7 units

38.

Find the distance between the two points.

a)

7.6 units

b)

6.9 units

c)

8.1 units

d)

9.7 units

39.

Find the direct distance between the court house and the town hall.

a)

26

b)

6.8

c)

10

d)

7.2 km

40.

Find the distance between these two points.

a)

13

b)

7.9

c)

9.2

d)

3.6

41.

Find the distance between (1,2) (-1,-2)

a)

4.5

b)

4.4

c)

5

d)

20

42.

What's the distance between (-3,4) and (-3, -10)?

a)

14

b)

-14

c)

6

d)

-6

43.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

44.

Which point is located at (2,-2)

a)

A

b)

B

c)

C

d)

D

45.

Find the length of the line segment.

a)

8

b)

7

c)

6

d)

5

46.

Find the distance between the points.

a)

3

b)

4

c)

5

d)

6

47.

What error did the student make when plotting the point (3, 4) according to the picture?

a)

The student moved left along the x-axis when he should have moved right

b)

The student plotted the y-coordinate in place of the x-coordinate

c)

The student didn't make a mistake

d)

Both Options 1 and 2

48.

If you were to plot the point (4, -12) what would be the correct method?

a)

Up 4, left 12

b)

Right 4, up 12

c)

Down 4, left 12

d)

Right 4, down 12

49.

If you were to plot the point (-2, -6) what would be the correct method?

a)

Down 2 , Left 6

b)

Left 6, Down 2

c)

Left 2, Down 6

d)

Left 2, Up 6

50.

The origin is where the x-axis and y-axis intersect

a)

True

b)

False

51.

The coordinates of a point are (y, x)

a)

True

b)

False

52.

Which point is NOT like the rest?

a)

(-3, -5)

b)

(-2, -2)

c)

(1, 7)

d)

(-6, -9)

53.

Which point is NOT like the rest?

a)

(-3, 5)

b)

(6, -2)

c)

(-1, 7)

d)

(-8, 9)

54.

Which letter matches the coordinate (4, -6)?

a)

G

b)

Z

c)

K

d)

None of the above

55.

Which letter matches the coordinate (0, -6)?

a)

O

b)

L

c)

i

d)

Z

56.

If you plotted the point (0, -7), you would be __________.

a)

on the y-axis.

b)

on the x-axis.

c)

in Quadrant I.

d)

in Quadrant II

57.

What letter is at (7, -6)?

a)

D

b)

L

c)

X

d)

There is no letter at those coordinates.

58.

Identify the ordered pair that represents point y.

a)

(5,-3)

b)

(-3,5)

c)

(1,-2)

d)

(1,-3)

59.

Identify the ordered pair that represents point x.

a)

(5,-3)

b)

(-3,5)

c)

(3,-1)

d)

(1,-3)

60.

Points G, H, and I are plotted on the coordinate grid. How many units are between points G and H?

a)

15 units

b)

14 units

c)

10 units

d)

9 units

61.

Find the distance between the two ordered pairs.

a)

5 units

b)

6 units

c)

7 units

d)

10 units

62.

What are the coordinates for point N

a)

(7,9)

b)

(-7,7)

c)

(-9,-7)

d)

(7, 7)

63.

Find the distance between the points (7,7) and (7,2)

a)

9

b)

0

c)

5

d)

-5

64.

Find the distance between the points (2,4) and (8,4)

a)

6

b)

10

c)

8

d)

-6

65.

Find the distance between the points (6,9) and (6,-5)

a)

4

b)

12

c)

-4

d)

14

66.

Find the distance between the points (2,5) and (-9,5)

a)

10

b)

11

c)

7

d)

-11

67.

Find the distance between the points (-3, 10) and (-2, 10)

a)

20

b)

5

c)

-5

d)

1

68.

Find the distance between the points (-5,5) and (-5,-10)

a)

-15

b)

15

c)

10

d)

-10

69.

Find the distance between the points (-8,-6) and (2,-6)

a)

12

b)

-10

c)

10

d)

-12

70.

Find the distance between (6,3) and (6,-10)

a)

12

b)

60

c)

3

d)

13

71.

Find the distance between the points (-10,10) and (-4,10)

a)

14

b)

6

c)

20

d)

1

72.

Find the distance between (7,7) and (7,-5)

a)

12

b)

14

c)

2

d)

-12

73.

a)

2.6 mi

b)

1.9 mi

c)

1.4 mi

d)

2.3 mi

74.

a)

32.5 ft

b)

40 ft.

c)

31 ft.

d)

33.5 ft.

75.

a)

F

b)

G

c)

H

d)

J

76.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

77.

solve for c

a)

7

b)

9

c)

4

d)

13

78.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew? (Round to the nearest tenth.)

a)

7.5 in

b)

12.4 in

c)

13.6 in

d)

14.3 in

79.

a)

A

b)

B

c)

C

d)

D

80.

a)

F

b)

G

c)

H

d)

J

81.

Which measurements could not represent the side lengths of a right triangle?

a)

6cm, 8cm, 10cm

b)

12cm, 35cm, 37 cm

c)

4cm, 6cm, 10cm

d)

10cm, 24cm, 26cm

82.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

83.

Find side "h" (wall height)

a)

35.60

b)

35.00

c)

35.71

d)

61.03

84.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

85.

Which Pythagorean Triple does the picture illustrate?

a)

4, 5, 6

b)

2, 3, 4

c)

3, 4, 5

d)

1, 2, 3

86.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

75 cm²

b)

105 cm²

c)

135 cm²

d)

30 cm²

87.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

88.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Round to the whole number.

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

89.

The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 3 feet tall and 6 feet wide?

a)

18

b)

6.7

90.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

91.

Find the perimeter of a triangle that has legs that are 3 cm and 4 cm.

a)

5

b)

7

c)

10

d)

12

92.

Which of the following sentences would belong in the proof that describes this image?

a)

The sum of the areas of the two smaller squares is equal to the area of the large square.

b)

The sum of the side lengths of the two smaller squares is equal to the side length of the large square.

c)

The difference of the areas of the two smaller squares is equal to the area of the large square.

d)

The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

93.

We are given one of the sides and the hypotenuse.

Find the length of the missing side length.

(Hint: distance from the wall to the bottom of the ladder)

a)

7

b)

5

c)

11

d)

25

94.

Which measurements could not represent the side lengths of a right triangle?

a)

6 cm, 8 cm, 10 cm

b)

12 cm, 35 cm, 37 cm

c)

4 cm, 6 cm, 10 cm

d)

10 cm, 24 cm, 26 cm

95.

a)

32.5 ft

b)

40 ft.

c)

31 ft.

d)

33.5 ft.

96.

a)

51 cm

b)

40.8 cm

c)

27 cm

d)

37.1 cm

97.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

98.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

99.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

100.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

101.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

102.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

103.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

104.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

105.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

106.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

a)

7.5 in

b)

12.4 in

c)

13.6 in

d)

14.3 in

107.

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

108.

what is the missing length?

a)

50

b)

60

c)

70

d)

80

109.

solve for c

a)

7

b)

9

c)

4

d)

13

110.

Round to the nearest hundredth.

a)

5.57

b)

10.63

c)

5.32

d)

9

111.

Do the segment lengths 9, 12, and 15 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

112.

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

a)

9

b)

40

c)

41

113.

Do these 3 side lengths form a right triangle?
13, 80, and 81?

a)

yes

b)

no

114.

Which set of side lengths form a right triangle?

a)

3, 4, 7

b)

33, 56, 65

c)

66, 72, 97

d)

10, 15, 25

115.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

116.

a = 2.1, b = 7.2, c = 7.5
Is this a right triangle?

a)

yes

b)

no

117.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

118.

a)

7 ft

b)

5 ft

c)

3 ft

d)

2 ft

119.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

120.

What is the height of the cone?

a)

14 cm

b)

8 cm

c)

12 cm

d)

13.9 cm

121.

if a = 3 feet, b = 8 feet, and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?

a)

8.54 feet

b)

10.44 feet

c)

10 feet

d)

4.12 feet

122.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

123.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

124.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

125.

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

126.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

127.

you ADD a² and c² then take the square root to find b on a right triangle.

a)

true

b)

false

128.

you ADD a² and b² then take the square root to find c on a right triangle.

a)

true

b)

false

129.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

130.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

131.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

132.

a)

The top of the ladder is 8.9 ft from the ground

b)

The top of the ladder is 9.2 ft from the ground

c)

The top of the ladder is 16.5 ft from the ground

d)

The top o the ladder is 14.4 ft from the ground

133.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

134.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

135.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

136.

_{^{Find the missing side}}

a)

√29.2

b)

√400

c)

√20

d)

√10

Unit 5: Pythagorean Theorem

Total questions: 136

Worksheet time: 13hrs 4mins

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