Download Section 5.7 Worksheet

Name _______________________________________ Date ___________________ Class __________________
Section 5.7
The Pythagorean Theorem
The Pythagorean Theorem states that the following relationship exists among the lengths of
the legs, a and b, and the length of the hypotenuse, c, of any right triangle.
a2 + b2 = c2
Use the Pythagorean Theorem to find the value of x in each triangle.
a2 + b2 = c2
Pythagorean Theorem
a2 + b2 = c2
x2 + 62 = 92
Substitute.
x2 + 42 = (x + 2)2
x2 + 36 = 81
Take the squares.
x2 + 16 = x2 + 4x + 4
x2 = 45
x=
45
x= 3 5
4x = 12
Simplify.
x=3
Take the positive
square root and
simplify.
Find the value of x. Give your answer in simplest radical form.
1.
2.
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3.
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4.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Section 5.7
The Pythagorean Theorem continued
A Pythagorean triple is a set of three
nonzero whole numbers a, b, and c
that satisfy the equation a2 + b2 = c2.
Pythagorean
Triples
Not Pythagorean
Triples
3, 4, 5,
5, 12, 13
2, 3, 4
6, 9, 117
You can use the following theorem to classify triangles by their angles if you know their side
lengths. Always use the length of the longest side for c.
Pythagorean Inequalities Theorem
m∠C < 90°
m∠C > 90°
If c2 > a2 + b2, then ∆ABC is obtuse.
If c2 < a2 + b2, then ∆ABC is acute.
Consider the measures 2, 5, and 6. They can be the side lengths of a triangle since
2 + 5 > 6, 2 + 6 > 5, and 5 + 6 > 2. If you substitute the values into c2 < a2 + b2, you
get 36 > 29. Since c2 > a2 + b2, a triangle with side lengths 2, 5, and 6 must be obtuse.
Find the missing side length. Tell whether the side lengths form a
Pythagorean triple. Explain.
5.
6.
Tell whether the measures can be the side lengths of a triangle.
If so, classify the triangle as acute, obtuse, or right.
7. 4, 7, 9
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10. 9, 12, 15
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8. 10, 13, 16
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11. 5, 14, 20
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9. 8, 8, 11
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12. 4.5, 6, 10.2
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Section 5.7
1. x = 12
2. x =
3. x =
4. x = 40
39
29
5. 10; yes; the three side lengths are
nonzero whole numbers that satisfy
a2 + b2 = c2.
6.
95; no;
7. yes; obtuse
9. yes; acute
11. no
95 is not a whole number.
8. yes; acute
10. yes; right
12. yes; obtuse
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry