Pythagorean Triples Worksheet
Explore and identify Pythagorean Triples, understand their properties, and apply them to solve geometric problems in this Grade 11 math worksheet.
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Pythagorean Triples Worksheet
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Read each question carefully and provide the best answer. Show all your work for short answer and matching questions.
1. Which of the following sets of numbers forms a Pythagorean Triple?
(2, 3, 4)
(5, 12, 13)
(6, 8, 9)
(10, 15, 20)
2. If (3, 4, 5) is a Pythagorean Triple, which of the following is also a Pythagorean Triple?
(6, 7, 8)
(9, 12, 15)
(1, 2, 3)
(10, 13, 16)
3. A set of three positive integers a, b, and c such that a² + b² = c² is known as a .
4. The most common primitive Pythagorean Triple is .
5. Determine if the set of numbers (8, 15, 17) forms a Pythagorean Triple. Show your work.
6. A ladder is 25 feet long. The base of the ladder is 7 feet from a wall. How high up the wall does the ladder reach? Identify the Pythagorean Triple formed.
7. All Pythagorean Triples are primitive.
True
False
8. A primitive Pythagorean Triple is a set of integers (a, b, c) such that a, b, and c have no common divisor other than 1.
True
False
Match the Pythagorean Triple with its type.
9. (3, 4, 5)
a. Non-primitive
10. (6, 8, 10)
b. Primitive
11. Explain how Euclid's formula (m² - n², 2mn, m² + n²) can be used to generate Pythagorean Triples, where m and n are positive integers with m > n, and m and n are coprime and not both odd. Provide an example.