This document contains information about Pythagorean triples and examples of working through problems involving right triangles and the Pythagorean theorem (a2 + b2 = c2). It includes: 1. A definition of Pythagorean triples as any three positive integers that satisfy the Pythagorean theorem formula. Examples are provided. 2. Notes that multiplying or dividing a Pythagorean triple by the same number results in another Pythagorean triple. An example is shown. 3. Practice problems are provided asking students to determine if given triangles are right triangles based on the lengths of their sides, and to find missing side lengths of right triangles in radical form. 4. Discussion questions are included about why

1. AIM: Pythagorean Triples
Do Now
I rented a car for 35 dollars a day with a government fee
of 2 dollars. If I have 422 dollars budgeted to rent the
car, how many days can I rent it?
EQUATION: _________________
Solve:
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2. Homework: Pages 452-453 #3, 6-8 all, 11, 12
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3. Guest Speaker
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4. Anticipatory Set
Matt rides his bike 12 miles west. Then he turns north and rides
another 20 miles before he stops to rest. How far is Matt from
his starting point when he stops to rest? (Draw a diagram to help
you with this problem)
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5. Find the missing sides of the following right
triangles and leave the answer in radical form.
7 in
4 in
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6. Find the missing sides of the following right
triangles and leave the answer in radical form.
9 cm
24 cm
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7. Pythagorean Triples
Any three positive integers that satisfy the formula
a2 + b2 = c2 form a Pythagorean triple.
a2 + b2 = c2
32 + 42 = 52 5
9 + 16 = 25 4
25 = 25
3
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8. When you multiply or divide a Pythagorean triple by the
same number, you get another Pythagorean triple.
So, (3 • 2, 4 • 2, 5 • 2), or (6, 8, 10), is a Pythagorean triple.
a2 + b2 = c2
62 + 82 = 102 10
36+ 64 = 100
8
100 = 100
6
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9. Can you find another Pythagorean Triples?
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10. 1.) Determine whether a triangle with the following side lengths would
be a right triangle individually. SHOW YOUR WORK.
2.) Discuss with your partner until agreement.
A.) 7 25 24 B.) 18 9 15
a2 + b2 = c2 a2 + b2 = c2
9 15 18
7 24 25
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11. 1.) Determine whether a triangle with the following side lengths would
be a right triangle individually. SHOW YOUR WORK.
2.) Discuss with your partner until agreement.
A.) 3 8 12 B.) 15 17 8
a2 + b2 = c2 a2 + b2 = c2
3 8 15 17
8 12
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12. Extra Practice
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13. BEFORE YOU LEAVE
The Babylonian Tablet Plimpton 322 was originally
written about 1800 BCE. This tablet contained a partial
list of Pythagorean Triples. Why do you think the
Babylonians wrote down this information and how do you
think they used their knowledge of Pythagorean Triples?
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14. Mr. Tjersland's Math 7
Homework: Pages 452-453 #13, 14, 20
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15. 15