Converse of Pythagoras Theorem Worksheet
Determine if a triangle is a right-angled triangle using the Converse of Pythagoras Theorem.
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Converse of Pythagoras Theorem
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Read each question carefully and use the Converse of Pythagoras Theorem to determine if the given triangles are right-angled triangles. Show all your work.
1. The sides of a triangle are 7 cm, 24 cm, and 25 cm. Is this a right-angled triangle? Show your work.
2. A triangle has sides measuring 8 inches, 15 inches, and 17 inches. Is it a right-angled triangle? Explain your reasoning.
3. Which set of side lengths could form a right-angled triangle?
3, 4, 6
5, 12, 13
6, 8, 9
7, 9, 11
4. If a triangle has side lengths a, b, and c, and a² + b² = c², what kind of triangle is it?
Acute
Obtuse
Right-angled
Equilateral
5. According to the Converse of Pythagoras Theorem, 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.
6. If a triangle has sides 10, 24, and 26, then 10² + 24² = , and 26² = . Therefore, it is a right-angled triangle.
7. A triangle with side lengths 9 cm, 40 cm, and 41 cm is a right-angled triangle.
True
False
8. The Converse of Pythagoras Theorem can be used to find the length of a missing side in any triangle.
True
False
9. A carpenter is building a rectangular frame. The sides measure 6 feet and 8 feet. If the diagonal measures 10 feet, is the frame perfectly rectangular (meaning it has a right angle)?
10. Sarah walks 5 blocks east and 12 blocks north. If she walks directly from her starting point to her ending point, forming a triangle with her path, how many blocks did she walk in the direct path? Is the triangle formed a right-angled triangle? Show your calculations.