We try the Pythagorean theorem which holds true
for and only for right triangles:
+ =
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A triangle with lengths 2, 3, 4
2² + 3² ≟ 4²
4 + 9 ≟ 16
13 ≟ 16
No, the Pythagorean theorem does not work, so a
triangle with sides 2,3,4 is not a right triangle.
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B. A triangle with lengths 6 inches, 8 inches, 10 inches
6² + 8² ≟ 10²
36 + 64 ≟ 100
100 ≟ 100
Yes, the Pythagorean theorem works, so a
triangle with sides 6,8,10 is a right triangle.
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C. A triangle with lengths 7, 12, 13
7² + 12² ≟ 13²
49 + 144 ≟ 169
193 ≟ 169
No, the Pythagorean theorem does not work, so a
triangle with sides 7,12,13 is not a right triangle.
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D. A triangle with lengths 8, 15, 17
8² + 15² ≟ 17²
64 + 225 ≟ 289
289 ≟ 289
Yes, the Pythagorean theorem works, so a
triangle with sides 8,15,17 is a right triangle.
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Edwin