Download Right Triangles

Teacher Key
Geometry
Right Triangles
Use the Pythagorean theorem to find the length of the hypotenuse. Show your work.
If the answer is not a perfect square, leave your answer in square root form.
13 cm
x = _____
x
5 cm
A.
15 inches
B.
20 feet
c
y
C.
8 inches
12 cm
17 inches
c = _____
82 + 152 = c2
64 + 225 = c2
289 = c2
17 = c
29 feet
y = _____
202 + 212 = y2
400 + 441 = y2
841 = y2
29 = y
53 cm
a = _____
22 + 72 = a2
4 + 49 = a2
53 = a2
53 = a
21 feet
a
2 cm
D.
7 cm
© 2003 CompassLearning, Inc.
52 + 122 = x2
25 + 144 = x2
169 = x2
13 = x
Activity 67252
Teacher Key
Geometry
Right Triangles
16 feet
20 feet
h = _____
12 feet
E.
h
5 inches
F.
k
61 inches
k = _____
162 + 122 = h2
256 + 144 = h2
400 = h2
20 = h
62 + 52 = k2
36 + 25 = k2
61 = k2
61 = k
6 inches
c
G. 6 cm
10
c = _____ cm
8 cm
2 inches
H. 3 inches
w
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82 + 62 = c2
64 + 36 = c2
100 = c2
10 = c
11
w = _____ inches
( 2 )2 + 32 = w2
2 + 9 = w2
11 = w2
11 = w
Activity 67252
Teacher Key
Geometry
Right Triangles
Extension
The Pythagorean theorem can also be used to find the leg of a right triangle when the
length of the hypotenuse and the other leg are known.
26 cm
b
10 cm
Subtract the value of the squared leg from both sides to isolate the unknown value.
a2 + b2 = c2
a – a2 + b2 = c2 – a2
0 + b2 = c2 – a2
b2 = c2 – a2
2
Substitute the known values into the formula.
a = 10 cm
c = 26 cm
b2 = c2 – a2
b2 = 262 – 102
Find the squares of the numbers.
b2 = 262 – 102
b2 = 676 – 100
Find the difference.
b2 = 676 – 100
b2 = 576
Find the square root of the difference to solve for the variable.
b2 = 576
2
b = 576
b = 24
© 2003 CompassLearning, Inc.
Activity 67252
Teacher Key
Geometry
Right Triangles
Use the Pythagorean theorem to find the length of the missing leg. Show your work.
If the answer is not a perfect square, leave your answer in square root form.
I.
9 cm
b = _____
15 cm
b
12 cm
J.
12 inches
K.
17 feet
6 inches
b
a
108 inches
b = _____
62 + b2 = 122
b2 = 122 - 62
b2 = 144 - 36
b2 = 108
b = 108
8 feet
a = _____
a2 + 152 = 172
a2 = 172 – 152
a2 = 289 – 225
a2 = 64
a=8
36 cm
a = _____
a2 + 152 = 392
a2 = 392 – 152
a2 = 1521 – 225
a2 = 1296
a = 36
15 cm
15 feet
L.
© 2003 CompassLearning, Inc.
39 cm
a
122 + b2 = 152
b2 = 152 – 122
b2 = 225 – 144
b2 = 81
b =9
Activity 67252
Teacher Key
Geometry
Connections
Think About It
Using what you know about the Pythagorean theorem, explain how you could tell if, given
the lengths of three sides of a triangle, that triangle was a right triangle.
SAMPLE RESPONSE: The Pythagorean theorem says that the sum of the squares of
________________________________________________________________________
the two legs is equal to the square of the hypotenuse. So, if you have three numbers
________________________________________________________________________
that represent the three side lengths of a triangle, you could square all three of them
________________________________________________________________________
and then check to see if two of the squared numbers add up to the third. If so, the
________________________________________________________________________
assumption can be made that the original three side lengths represented the lengths
________________________________________________________________________
of the sides of a right triangle.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Pythagorean Triple
A Pythagorean triple consists of three whole numbers that satisfy the equation a2 + b2 = c2,
where c is the largest number. An example is the triple 3-4-5, where 32 + 42 = 52.
Experiment with whole numbers to generate a list of as many Pythagorean triples as you
can discover.
Sample Response: There are an infinite number of Pythagorean triples.
3-4-5
6-8-10
5-12-13
8-15-17
12-16-20
17-24-25
10-24-26
© 2003 CompassLearning, Inc.
Activity 67252