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Justification: See Solution
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Converse of the Pythagorean Theorem |
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If the sides of a triangle have lengths a, b, and c, and c^2=a^2+b^2, then the triangle is a right triangle. |
This tells us that we can use the Pythagorean Theorem in reverse to test if a triangle is right. In general, the hypotenuse c has the greatest value. Let's substitute a=12, b=12, and c=12 into a^2+b^2=c^2, and see if they produce a true statement.
Substitute values
Calculate power
Add terms
The values produce a false statement, so the described triangle is not a right triangle.
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Converse of the Pythagorean Theorem |
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If the sides of a triangle have lengths a, b, and c, and c^2=a^2+b^2, then the triangle is a right triangle. |
This tells us that we can use the Pythagorean Theorem in reverse to test if a triangle is right. In general, the hypotenuse c has the greatest value. Let's substitute a=5, b=12, and c=13 into a^2+b^2=c^2, and see if they produce a true statement.
Substitute values
Calculate power
Add terms
The values produce a true statement, so the described triangle is a right triangle.