Converse of Pythagoras Theorem Worksheet
Explore the Converse of Pythagoras Theorem with this worksheet for Grade 9 students, featuring multiple choice, fill-in-the-blanks, and short answer questions.
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Converse of Pythagoras Theorem
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
1. Which of the following sets of side lengths could form a right-angled triangle?
3, 4, 6
5, 12, 13
7, 8, 9
2, 3, 4
2. If a triangle has sides of length a, b, and c, and a² + b² = c², then the triangle is:
Acute-angled
Obtuse-angled
Right-angled
Equilateral
3. The Converse of Pythagoras Theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a triangle.
4. If a triangle has sides 6 cm, 8 cm, and 10 cm, then 6² + 8² = , and 10² = , so the triangle is a right-angled triangle.
5. A triangle with sides 9, 12, and 15 is a right-angled triangle.
True
False
6. The Converse of Pythagoras Theorem can be used to find the length of a missing side in a right-angled triangle.
True
False
7. A triangle has sides of length 8 cm, 15 cm, and 17 cm. Use the Converse of Pythagoras Theorem to determine if it is a right-angled triangle. Show your work.
8. Consider the triangle with side lengths 6, 8, and 10 units shown above. Explain how you would use the Converse of Pythagoras Theorem to verify if it is a right-angled triangle.
9. A carpenter is building a rectangular frame. He measures the sides as 30 inches and 40 inches. He then measures the diagonal to be 50 inches. Is the frame perfectly rectangular? Explain your reasoning using the Converse of Pythagoras Theorem.