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WorksheetsPythagorean Theorum
Total questions: 201
Worksheet time: 12hrs 52mins
a2 + b2 + c2
Sides a and b are called legs.
true
false
Side c on a right triangle is ALWAYS the longest.
true
false
If the side lengths of a right triangle are 7, 25, and 24, which side is the hypotenuse?
7
25
24
none of the these
If the sides of a right triangle are 40, 50, and 30, which sides are the legs?
40 and 50
50 and 30
40 and 30
30, 40, and 50
a=3, b=4, and c=5
Is this a right triangle?
yes
no
a=6, b=8, and c=10
Is this a right triangle?
yes
no
Which side lengths would form a right triangle?
3, 5, 6
2, 8, 10
3, 4, 5
7, 12, 15
The Pythagorean Theorem is (a) (b) (c) (d) (e)
a2
+
b2
=
c2
x2
−
×
÷
What letter represents the hypotenuse?
a
b
a and b
c
Hypotenuse
Vertical side in a right triangle
Longest side in a right triangle
Horizontal side in a right triangle
a2 + b2 = c2
Which choice represents the legs?
a and b
a
b
c
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
The Pythagorean Theorem is
a2 - b2 = c2
false
true
Side c on a right triangle is ALWAYS the longest.
true
false
Side a on a right triangle is ALWAYS the longest side
true
false
If you are solving to find a missing leg, should you add or subtract?
Add
Subtract
If you are solving to find a missing hypotenuse, should you add or subtract?
Add
Subtract
9
41
6.4
3
Level 2
Solve for the value of y
13
5
23
10
13
7.9
9.2
3.6
Draw a right triangle and label the sides using: Leg, Leg, Hypotenuse

Level 1
The Pythagorean Theorem ONLY works on which triangle?
obtuse
scalene
isosceles
right
Level 1
The Pythagorean Theorem is
a2 + b2 + c2
false
true
Level 1
If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?
6
6.7
3
15.7
None of them
Level 2
Solve for the value of y
13
5
23
10
−√36
±6
+ 6 only
+ 18
Not Possible
a2 + b2 + c2
Sides a and b are called legs.
true
false
Side c on a right triangle is ALWAYS the longest.
true
false
What is the relationship between the sides in the Pythagorean Theorem shown?
a + b = c
a2 + b2 = c2
a2 – b2 = c2
a – b = c
c = 7.5
Is this a right triangle?
What is the relationship between the sides in the Pythagorean Theorem shown?
a + b = c
a2 + b2 = c2
a2 – b2 = c2
a – b = c
What is the length of the missing side?
3
8
12
18
What is the length of the missing side?
x = 4
x = 8
x = 10
x = 16
Which equation reflects the right triangle shown?
x2 + 142 = 202
142 + 202 = x2
142 – 202 = x2
x2 – 142 = 202
Which equation can be used to solve for "x"?
152 – x2 = 212
x2 – 152 = 212
152 + 212 = x2
212 – 152 = x2
Which Pythagorean Triple does the picture illustrate?
4, 5, 6
2, 3, 4
3, 4, 5
1, 2, 3
Find the value of "c"
c = 8
c = 10
c = √52
c = √20
Determine the length of the missing side.
7
8
17
23
Which equation can NOT be used to find the length of the missing side?
122 + 132 = x2
x2 + 122 = 132
132 – 122 = x2
132 – x2 = 122
What is the length of the hypotenuse in the triangle shown?
3
4
5
8
The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse?
13
14
26
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?
8 feet
5.29 feet
10 feet
14 feet
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?
12 feet
13.9 feet
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)
180 feet
90 feet
13.4 feet
127.3 feet
A metal bar is being added to a jungle gym, what is the length the added metal bar?
5.4
2.6
3.2
7.9
What is the length of the segment A to G?
6.16
3.63
12.7
8
What is the distance between Point A and point B?
26
12
18
24
The Pythagorean Theorem only works for ________ triangles.
Scalene
Obtuse
Equilateral
Right
Sides a and b are called the (a)
Side c (the hypotenuse) is always the (a) side.
The side that is missing is
the hypotenuse
a leg
Nothing
a right angle
The side that is missing is
the hypotenuse
a leg
We aren't missing a side
the right angle
Find the missing side.
Round your answer to the nearest tenth.
(a)
Find the missing side length. Round your answer to the nearest tenth.
(a)
How far up the building does the ladder reach? Round your answer to the nearest tenth.
(a)
How far would it be if you ran diagonally across the field? Round your answer to the nearest tenth.
(a)
Find the length of the missing side
3
41
41
9
How long is the zip line?
70
2900
70
2900
True or False: The Pythagorean Theorem can be used to solve acute or obtuse triangles.
True
False
Determine the length of the missing side.
7
8
17
23
Which equation can be used to solve for "x"?
x2 + 152 = 212
x2 – 152 = 212
152 + 212 = x2
x2 + 212 = 152
Side c on a right triangle is ALWAYS the longest.
True
False
Find the missing side
9
41
6.4
3
The slide at a playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. To find the length of the slide, which diagram would I use?
Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?
44.1 km
59 km
47.8 km
33 km
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?
9 feet
19.2 feet
81 feet
369 feet
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?
12 feet
13.9 feet
The Pythagorean Theorem ONLY works on which triangle?
obtuse
scalene
isosceles
right
What side(s) will always be the longest on a right triangle?
The Hypotenuse
Leg A
Leg B
The Right Angle
What side(s) will always be the shortest on a right triangle?
Select all that apply
The Hypotenuse
Leg A
Leg B
The Right Angle
What is the relationship between the sides in the Pythagorean Theorem shown?
Hint: Think about when the hypotenuse is missing!
a + b = c
a2 + b2 = c2
a2 – b2 = c2
a – b = c
13, 80, and 81?
If the sides of a triangle are 7, 24, and 25, is it a right triangle?
c = 7.5
Is this a right triangle?
How long is the hypotenuse of this triangle?
(a)
Is this a right triangle?
Yes
No
Is this a right triangle?
Yes
No
Is this a right triangle?
Yes
No
Is a triangle with side lengths of 12, 9, and 15 a right triangle?
Yes
No
Is a triangle with side lengths of 7, 4, and 4 a right triangle?
Yes
No
Find the missing side.
18
16
17
19
Find the missing side.
11
12
13
14
A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?
23
26
28
25
Before we start, I would like you to find out what the (6)2 is. (please use a calculator.
(a)
Now find out what 32 using the calculator.
(a)
What number is the hypotenuse
15
17
8
hypotenwhose?
1
Find the value of x. Round to the nearest hundredth.
examples 2.145 would be 2.15
(a)
Solve for the missing side. Round to the nearest hundredth.
(a)
Find the value of x... You should NOT get a decimal.
(a)
Find the length of the missing side. (no decimal)
(a)
Find the value of the missing side. (No decimal)
(a)
Find the value of the missing side. (No Decimal)
(a)
Sides a and b are called legs.
true
false
Side c on a right triangle is ALWAYS the longest.
true
false
The Pythagorean Theorem states that if you have a right triangle, then...
a3+b3=c3
a2+b2=c2
b2+c2=a2
2a+2b=2c
What is the side length of the square?
10 units
50 units
25 units
94 units
What is the missing side length?
98 units
49 units
13 units
14 units
What is the missing area?
22 square units
121 square units
44 square units
5.5 square units
Which side is the hypotenuse?
red
blue
purple
Elizabeth is trying to find the missing side length. Here is her work. What mistake did she make?
She added incorrectly. 3+4 is not 7.
She added the side lengths instead of the areas. She should square 3 and 4 BEFORE adding.
She used the wrong hypotenuse. 4 is the longest side.
She should multiply 3 and 4 to get 12.
What is the missing area?
64 square units
6 square units
164 square units
36 square units
What is the missing area?
13 square units
169 square units
119 square units
50 square units
What is the missing area?
49 square units
7 square units
25 square units
5 square units
What is the missing side length?
4.5 units
41 units
3 units
9 units
What is the missing side length?
25 units
5 units
7 units
12.5 units
4, 5, 6
The Pythagorean Theorem is a Geometry rule that applies to the side lengths of a (a) .
Do you prefer to solve for missing side lengths by drawing area squares or by using the equation?
Drawing area squares
With the equation
Either way works for me
How tall would the ladder in the picture need to be to reach the house?
36 feet
29 feet
39 feet
43 feet
Using the triangle pictured here: what would the length of side c equal?
23.2
24.19
25.29
25
The lengths of the sides of a triangle are 3, 2.5 and 3.5. Is this triangle a right triangle?
Yes
No
Which of the triangles below are considered right triangles? (Select one or more from the options below).
Triangle 1: 10, 24 and 26
Triangle 2: 8, 6, and 14
Triangle 3: 6, 8 and 10
Solve for x. x=32
(a)
Solve for x. x=−62
(a)
What is the square root of 25?
25 =?
(a)
How many square units are in square A, B, and C?
What can you tell me about the relationship between the area of these three squares?
Brianna is planting a sapling. The garden center recommended she stabilize the sapling with guide wires for the first year.
6.6 feet
7.8 feet
12.2 feet
15.6 feet
13
7.9
9.2
3.6
What is the formula for the Pythagorean Theorem?
c2 = a2 + b2
a3 + b3 = c3
a2 + b2 = c2
c3 = a3 + b3
The areas of the two smaller squares are shown in the diagram. Which expression can be used to find the AREA of the largest square?
302+152
302+152
30+15
30+15
The area of the largest square and the area of one of the two smaller squares are shown in the diagram.
Which expression can be used to find the AREA of the second smaller square?
105−30
105+30
1052+302
1052−302
Three squares are created using the side lengths of a right triangle. Which equation is modeled by the diagram shown?
32 + 52 = 42
32 + 42 = 52
52 + 42 = 32
92 + 162 = 252

12 in2
144 in2
194 in2
13.9 in2
What is the AREA of square ABCD?
16
20
25
25.3
The (a) of the (b) created by the legs of a (c) triangle are (d) to the area of the square created by the (e) .

12 in2
144 in2
194 in2
13.9 in2
The (a) of the (b) created by the legs of a (c) triangle are (d) to the area of the square created by the (e) .
What is the AREA of square ABCD?
16
20
25
25.3
Three squares are created using the side lengths of a right triangle. Which equation is modeled by the diagram shown?
32 + 52 = 42
32 + 42 = 52
52 + 42 = 32
92 + 162 = 252
The area of the largest square and the area of one of the two smaller squares are shown in the diagram.
Which expression can be used to find the AREA of the second smaller square?
105−30
105+30
1052+302
1052−302
The areas of the two smaller squares are shown in the diagram. Which expression can be used to find the AREA of the largest square?
302+152
302+152
30+15
30+15
