Pythagorean Triples Worksheet
Explore and identify Pythagorean triples, understand their properties, and apply them to solve geometric problems at a Grade 12 level.
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Pythagorean Triples Exploration
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = . These integers represent the side lengths of a triangle.
2. A primitive Pythagorean triple is one in which a, b, and c are to each other, meaning their greatest common divisor is .
3. Which of the following sets of numbers forms a Pythagorean triple?
(6, 8, 9)
(7, 24, 25)
(5, 12, 14)
(8, 15, 18)
4. Which of the following is a primitive Pythagorean triple?
(6, 8, 10)
(9, 12, 15)
(10, 24, 26)
(11, 60, 61)
5. A ladder is 17 feet long. If the base of the ladder is 8 feet from the wall, how high up the wall does the ladder reach? Identify the Pythagorean triple involved.
6. The diagonal of a rectangle is 25 cm. If one side of the rectangle is 7 cm, what is the length of the other side? What Pythagorean triple is demonstrated here?
7. Describe Euclid's formula for generating Pythagorean triples. Use the formula to generate two primitive Pythagorean triples.
8. All multiples of a Pythagorean triple are also Pythagorean triples.
True
False
9. Every right triangle has sides that form a Pythagorean triple.
True
False
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