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Pythagorean Theorem and its Converse

Total questions: 59

Worksheet time: 1hrs 26mins

Name
Class
Date
1.
Is this triangle a right triangle?
a)
yes
b)
no
2.
Do the sides 15, 30 and 34 make a right triangle?
a)
yes
b)
no
3.
If the legs of a right triangle are 16 and 63, what is the length of the hypotenuse?
a)
79
b)
2112.5
c)
65
d)
61
4.
If the sides of a triangle are 7, 24, and 25, is it a right triangle?
a)
yes
b)
no
5.
Which set of side lengths form a right triangle?
a)
4, 8, 12
b)
12, 13, 20
c)
20, 21, 29
d)
48, 55, 74
6.
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
7.
a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?
a)
yes 
b)
no
8.
Find the value of x.
a)
√33
b)
√29
c)
√35
d)
√41
9.
If the legs of a right triangle are 10 and 24, then the hypotenuse is __________.
a)
21
b)
19
c)
26
d)
30
10.
Simplify √24
a)
4√6
b)
2√6
c)
6√2
d)
2√12
11.
Simplify √125
a)
5√5
b)
25√5
c)
5√25
d)
5√2
12.
In simplest radical form,
√80 is equivalent to
a)
16√5
b)
2√20
c)
4√5
d)
8√5
13.
Simplify √16
a)
4
b)
8
c)
16
d)
64
14.
Find the missing side
a)
48
b)
108
c)
83.6
d)
72
15.
Find the EXACT value of x in simplified radical form if necessary.
a)
√8
b)
8
c)
2
d)
2√2
16.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
17.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know how to do this
18.
Find the value of x.
a)
2√5
b)
3√5
c)
4√5
d)
10√5
19.
Acute, right, or obtuse
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
20.
Simplify:
√45
a)
9√5
b)
3√5
c)
5√9
d)
3√15
21.
Simplify:
√27
a)
3√9
b)
9√3
c)
3√3
d)
27√1
22.
Simplify:
 
√120
a)
12√10
b)
2√60
c)
4√30
d)
2√30
23.
Simplify:
√96
a)
16√6
b)
6√16
c)
9√6
d)
4√6
24.
a)
A
b)
B
c)
C
d)
D
25.
a)
A
b)
B
c)
C
d)
D
26.

1. A 15 meter telephone pole is attached 8 meters away to the level ground by a 17 meter guy wire. Is the telephone pole perpendicular to the ground?

a)

Yes, it is perpendicular because there is a 90° angle

b)

No, it is not perpendicular because there is not a 90° angle

27.

A 75 foot wire is needed to connect the top of the antenna to the hook 15 ft from the base of the antenna. To the nearest tenth, how tall is the antenna?

(a)  

28.

The distance between consecutive bases in major league baseball is 90ft. Find the distance from home plate to second base. Round to the nearest whole number.

(a)  

29.

A frame measures 60 cm in length and 11 cm in width. If the diagonal measures 61 cm, do the corners of the frame meet at 90° angles?

a)

Yes, the corners meet at 90° angles

b)

No, the corners do not meet at 90° angles

30.

A surveyor had poles marked at points A, B, and C. The distances are shown. What is the approximate distance from A to C? Round to the nearest whole number.

(a)  

31.

Carla lives 20 miles due north of her favorite radio station. While driving due east from her house, she was able to keep the radio signal for about 75 miles. What is the broadcasting range of her favorite radio station? Round to the nearest tenth.

(a)  

32.

Lisa lives 28 miles due south of the city. Lisa also lives 45 miles due east of her friend Stacey. How far does Stacey live from the city?

(a)  

33.

An airplane is flying at an altitude of 4.1km. The plane’s slant distance from the runway is 15.1km. How far must the plane travel to be directly above the runway? Round to the nearest tenth.

(a)  

34.

An A-frame tent is in the shape of an isosceles triangle. The base of the triangle is 10 feet and the two congruent sides are 8 feet each. What is the height of the tent? Round to the nearest tenth.

(a)  

35.

A 10 foot ladder is leaning against a building. The bottom of the ladder is 5 feet from the building. How high is the top of the ladder? Round to the nearest tenth.

(a)  

36.

Joel walks from his house to the gas station to pick up a soda, then walks to school. How much shorter could his walk be if he cut across the path, instead?

(a)  

37.

The coordinates of segment MN are M(9,2) and N(6,7).  To the nearest tenth, what is the length of segment MN?



(a)  

38.

What letter represents the hypotenuse?

a)

a

b)

b

c)

a and b

d)

c

39.

Hypotenuse

a)

Vertical side in a right triangle

b)

Longest side in a right triangle

c)

Horizontal side in a right triangle

d)

a2 + b2 = c2

40.

Which choice represents the legs?

a)

a and b

b)

a

c)

b

d)

c

41.

Define the term 'right angle'

a)

Three angles in a right triangle

b)

When two angles in a triangle are 90 degrees

c)

Any angle less than 90 degrees

d)

A 90 degree angle

42.

The Pythagorean Theorem is _________

a)

a + b = c

b)

a2 + b2 = c2

c)

a2 + b2 + c2

d)

A = LW

43.

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

44.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

45.
Do the segment lengths 15, 12, and 9 form a right triangle?
a)
Yes
b)
No
c)
Maybe
d)
Pythagoras
46.
Do the segment lengths 15, 12, and 9 form a right triangle?
a)
Yes
b)
No
c)
Maybe
d)
Pythagoras
47.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

48.

The Pythagorean Theorem ONLY works on which triangle? 

a)

Obtuse

b)

Right

c)

Acute

d)

Isosceles

49.

What is the side of a right triangle across from the right angle called?

a)

Square

b)

Arm

c)

Leg

d)

Hypotenuse

50.

Side c on a right triangle is ALWAYS the longest.

a)

True

b)

False

51.

Find the length of the missing side

a)

17

b)

15

c)

22

d)

13

52.

Find the length of the missing side

a)

20

b)

68

c)

16

d)

80

53.

Is this a right triangle

a)

Yes

b)

No

54.

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

a)

172+82=b217^2+8^2=b^2  

b)

82+b2=1728^2+b^2=17^2  

c)

172+b2=8217^2+b^2=8^2  

d)

82b2=172100\frac{8^2}{b^2}=\frac{17^2}{100}  

55.

What is the opposite of squaring a number

a)

divide

b)

multiply

c)

square root

d)

fractions

56.

The Pythagorean is used to find what

a)

missing sides only

b)

missing angles only

c)

either missing sides or angles

57.
Which equation is modeled by the picture shown?
a)
32+52=42
b)
32+42=52
c)
52+42=32
d)
92+162=252
58.
Do these 3 side lengths form a right triangle?
13, 80, and 81?
a)
yes
b)
no
59.
If a = 9 and b = 7, what is c?
a)
130
b)
12.4
c)
11.4
d)
11

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