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Converse of the Pythagorean Theorem — Easy Worksheet 1
Grade 8 · MathSheets Name: ____________________ Date: __________
Decide whether each triangle is a right triangle. Write yes or no.
How to solve
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Example
A triangle has sides 4 cm, 3 cm and 5 cm. Is it a right triangle?
Answer: yes
Not quite. The answer is
💡 The longest side is 5. Check a2 + b2 = c2: 32 + 32 = 9 + 9 = 18 and 52 = 25. They are not equal, so it is not a right triangle. The answer is no.
✓ Correct!
Not quite. The answer is
💡 The longest side is 5. Check a2 + b2 = c2: 32 + 32 = 9 + 9 = 18 and 52 = 25. They are not equal, so it is not a right triangle. The answer is no.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has sides 3 cm, 4 cm and 5 cm. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 17. Check a2 + b2 = c2: 92 + 152 = 81 + 225 = 306 and 172 = 289. They are not equal, so it is not a right triangle. The answer is no.
✓ Correct!
Not quite. The answer is
💡 The longest side is 17. Check a2 + b2 = c2: 92 + 152 = 81 + 225 = 306 and 172 = 289. They are not equal, so it is not a right triangle. The answer is no.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has side lengths 5, 12, 13. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 62 + 122 = 36 + 144 = 180 and 132 = 169. They are not equal, so it is not a right triangle. The answer is no.
✓ Correct!
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 62 + 122 = 36 + 144 = 180 and 132 = 169. They are not equal, so it is not a right triangle. The answer is no.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has side lengths 4, 3, 4. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 4. Check a2 + b2 = c2: 32 + 42 = 9 + 16 = 25 and 42 = 16. They are not equal, so it is not a right triangle. The answer is no.
✓ Correct!
Not quite. The answer is
💡 The longest side is 4. Check a2 + b2 = c2: 32 + 42 = 9 + 16 = 25 and 42 = 16. They are not equal, so it is not a right triangle. The answer is no.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has sides 15 cm, 12 cm and 5 cm. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 52 + 122 = 25 + 144 = 169 and 132 = 169. They are equal, so it is a right triangle. The answer is yes.
✓ Correct!
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 52 + 122 = 25 + 144 = 169 and 132 = 169. They are equal, so it is a right triangle. The answer is yes.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has sides 15 cm, 17 cm and 8 cm. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 42 + 122 = 16 + 144 = 160 and 132 = 169. They are not equal, so it is not a right triangle. The answer is no.
✓ Correct!
Not quite. The answer is
💡 The longest side is 13. Check a2 + b2 = c2: 42 + 122 = 16 + 144 = 160 and 132 = 169. They are not equal, so it is not a right triangle. The answer is no.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has side lengths 5, 13, 12. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 5. Check a2 + b2 = c2: 32 + 42 = 9 + 16 = 25 and 52 = 25. They are equal, so it is a right triangle. The answer is yes.
✓ Correct!
Not quite. The answer is
💡 The longest side is 5. Check a2 + b2 = c2: 32 + 42 = 9 + 16 = 25 and 52 = 25. They are equal, so it is a right triangle. The answer is yes.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has side lengths 12, 12, 5. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The longest side is 17. Check a2 + b2 = c2: 82 + 152 = 64 + 225 = 289 and 172 = 289. They are equal, so it is a right triangle. The answer is yes.
✓ Correct!
Not quite. The answer is
💡 The longest side is 17. Check a2 + b2 = c2: 82 + 152 = 64 + 225 = 289 and 172 = 289. They are equal, so it is a right triangle. The answer is yes.
💡 How to solve: Converse of the Pythagorean Theorem
Square the two shorter sides and add them, then square the longest side. If a2 + b2 = c2 exactly, the triangle is a right triangle (the right angle is opposite the longest side). If the two results are different, it is not a right triangle.
Try a similar one
A triangle has sides 4 cm, 3 cm and 4 cm. Is it a right triangle?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Converse of the Pythagorean Theorem — Easy Worksheet 1
Decide whether each triangle is a right triangle. Write yes or no.