Converse of Pythagoras Theorem Worksheet
Explore the Converse of Pythagoras Theorem with this worksheet for Grade 6 students, featuring questions on identifying right triangles.
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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.
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (a² + b² = c²).
The Converse of the Pythagorean Theorem helps us determine if a triangle is a right-angled triangle. If a² + b² = c² for a triangle with sides a, b, and c (where c is the longest side), then the triangle is a right-angled triangle.
1. Which set of side lengths can form a right-angled triangle?
3, 4, 6
5, 12, 13
7, 8, 10
2, 3, 4
2. If a triangle has sides of length 8 cm, 15 cm, and 17 cm, is it a right-angled triangle?
Yes
No
Cannot be determined
Only if it's an isosceles triangle
3. The Converse of the Pythagorean 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. In a triangle with sides a, b, and c, if a² + b² = c², then the angle opposite side c is a angle.
5. A triangle has side lengths of 9 units, 40 units, and 41 units. Use the Converse of the Pythagorean Theorem to determine if it is a right-angled triangle. Show your work.
6. Draw a right-angled triangle and label its sides a, b, and c, with c being the hypotenuse.
7. If the sides of a triangle are 6, 8, and 10, it is a right-angled triangle.
True
False
8. The Converse of the Pythagorean Theorem can be used to find the length of a missing side in a right-angled triangle.
True
False
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