Question

Use the Converse to the Pythagorean Theorem to determine if the triangle below is a right triangle.

State whether or not the triangle is a right triangle.

Answer 1

not a right triangle

Explanation:

The side lengths do not meet the requirements of the Triangle Inequality. The given figure is not even a triangle.

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Additional comment

The triangle inequality requires the sum of the two short sides exceed the long side:

3 + 9 > 12 . . . . not true

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The converse of the Pythagorean theorem tells you that the triangle is a right triangle if the sum of the squares of the short sides is equal to the square of the long side: 3² +9² = 12² (not true). Here, that criterion is not met, so the triangle is not a right triangle.