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Pythagorean Theorem

Total questions: 48

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

The length of a shadow of a building is 29m. The distance from the top of the building to the tip of the shadow is 36m. The height of the building is (a)   m. If necessary, round your answer to the nearest tenth.

2.

Determine whether a triangle with the given side lengths is a right triangle.

Check all correct answers.

a)

14, 48, 50

b)

8, 14, 16

c)

10, 11,15

d)

5,12,13

3.

What is the length of the missing side?

a)

x = 4

b)

x = 8

c)

x = 10

d)

x = 16

4.

Which Pythagorean Triple does the picture illustrate?

a)

4, 5, 6

b)

2, 3, 4

c)

3, 4, 5

d)

1, 2, 3

5.
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
6.
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
7.
Is 10, 24, and 13 a Pythagorean triple?
a)
yes
b)
no
c)
cannot tell
8.
Classify this triangle by its sides. 
a)
equilateral
b)
scalene
c)
isosceles
d)
right
9.

Classify this triangle by its sides.

a)

equilateral

b)

scalene

c)

isosceles

10.
Classify this triangle by its angles.
a)
equiangular
b)
acute
c)
obtuse
d)
right
11.
State if the triangle is acute, obtuse, or right.
a)
acute
b)
obtuse
c)
right
12.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
13.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
14.
A triangle has side lengths:
5, 8, 6.  Is this triangle a right triangle, an acute triangle, or an obtuse triangle?
a)
right
b)
acute
c)
obtuse
15.
Acute, right, or obtuse?
1 , 2 , 3
a)
Right
b)
Obtuse
c)
Acute
d)
Not a triangle
16.
Find missing side
a)
5
b)
7
c)
9
d)
11
17.
What is the measure of x?
a)
12
b)
15
c)
6
d)
9
18.
Complete each proportion.
CB / DM  =  AC / ?
a)
BM
b)
MA
c)
BC
d)
AD
19.
To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown.  What is AB to the nearest meter?
a)
10
b)
12
c)
15
d)
18
20.
1.  Two triangles are similar, and the ratio of each pair of corresponding sides is 2:1. Which statement regarding the two triangles is not true?
a)
Their areas have a ratio of 4:1
b)
Their altitudes have a ratio of 2:1
c)
Their perimeters have a ratio of 2:1
d)
Their corresponding angles have a ratio of 2:1
21.

What is the length of the diagonal of the box shown below?

a)

7

b)

3

c)

7.28

d)

7.87

22.

What is the length of s?

a)

20.88 in

b)

20 in

c)

6 in

d)

19.01 in

23.

Find the length of the d.

a)

5.7

b)

3.6

c)

6

d)

7

24.

Find the length of x

a)

289

b)

17

c)

15.5

25.
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
26.
Find the endpoint of the segment with the endpoint of  (-4, 5) and midpoint of (7, -9) 
a)
(18, 13)
b)
(13, 18)
c)
(11,4)
d)
(1.5, -2)
27.
What is the midpoint between (-4,4) and (-2,2)?
a)
(3,2)
b)
(-3,3)
c)
(4,5)
d)
(6,7)
28.
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,8)   Midpoint (0,9)
a)
(-9, 10)
b)
(1.5, -1)
c)
(4.5, -0.5)
d)
(8.5, 4.5)
29.
Find the distance between the two points: (2, -1) and (2, 5)
a)
0
b)
8.3
c)
6
d)
5.5
30.
Find the y-coordinate of the midpoint of the line
a)
1
b)
2
c)
-2
d)
3
31.

The distance formula comes from the following equation:

a)

Midpoint Formula

b)

Circumference

c)

Slope Equation

d)

Pythagorean Theorem

32.

The hypotenuse of a right triangle is always across from:

a)

The adjacent side

b)

The opposite side

c)

The right angle

d)

The acute angle

33.

What is the perimeter of the playground

a)

52 yards

b)

520 yards

c)

13 yards

d)

260 yards

34.

What is the perimeter of the desk?

a)

44 inches

b)

78 inches

c)

88 inches

d)

90.2 inches

35.

What is the perimeter of the rectangle? (Round to the nearest tenth)

a)

18

b)

about 23.6

c)

about 25.1

d)

about 21.6

36.
Find the perimeter of the figure to the right.  Round to the nearest tenth.
a)
20.8 units
b)
116 units
c)
11.5 units
d)
19.8 units
37.

What is the area of the parallelogram?

a)

18 units2

b)

20 units2

c)

24 units2

d)

30 units2

38.
a)
True
b)
False
39.
(x, y) -------> (x - 3, y) is a translation of 3 units to the left.   
a)
True
b)
False
40.
A(-2, 2) and B(3, 2)
Rotate 180 degrees 
a)
A' (-2, 2), B' (3, 2)
b)
A' (-2, -2), B' (-3, -2)
c)
A' (2, -2), B' (-3, -2)
d)
A' (2, -2), B' (2, 3)
41.

Debbie is painting an image on a piece of art canvas. The image she is reproducing is 3 inches by 5 inches. She enlarges the dimensions 4 times. Which of the following statements is NOT true?

a)

The perimeter of the original image and the perimeter of the new image are related by a scale factor of 4.

b)

The area of the new image is 4 times the area of the original image.

c)

The area of the original image and the area of the new image are related by a scale factor of 16.

d)

The perimeter of the original image is 14\frac{1}{4} the perimeter of the new image.

42.

Which of the following images shows a rotation of 180o?

a)
b)
c)
d)
43.
Pablo throws a ball with a path of
h = -5(t - 2)2.
Maria throws a ball with a path of
h = -5(t - 2)2 + 10.
Which description is reasonable for the difference in the two equations?
a)
Maria throws the ball 10 times harder than Pablo does.
b)
Maria starts her ball at a height 10 feet higher than Pablo does.
c)
Pablo throws the ball 10 times harder than Maria does.
d)
Pablo starts his ball at a height 10 feet higher than Maria does.
44.
Match the description to its equation.
Moves up 2
Moves left 4
a)
A
b)
B
c)
C
d)
D
45.
Match the equation to its description.
a)
Reflected over x and up 4
b)
Reflected over x and down 4
c)
Reflected over x and right 4 
d)
Reflected over x and left 4
46.
Match the equation to its description.
a)
Stretched by 2 and up 4
b)
Compressed by 2 and up 4
c)
Stretched by 2 and left 4
d)
Compressed by 2 and left 4
47.

What makes isometric transformations different than similarity transformations?

a)

Isometric transformations have the same shape AND size, similarity transformations just have the same shape.

b)

Isometric transformations are cooler

c)

Isometric transformations have the same shape AND size, similarity transformations just have the same size.

d)

They are the same, no differences.

48.

Quad OBCD is similar to Quad OHTE because:

a)

Quad OBCD can be reflected over the x axis and then rotated 90 degrees

b)

Quad OBCD can be reflected over the x-axis and then dilated about point O by a scale factor of 2.

c)

Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 2.

d)

Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 1/2.

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