A triangle has exactly three sides. Prove the conditional by proving the contrapositive. If a polygon has more than three sides, then it is not a triangle. Contrapositive: If , then . Since , the contrapositive is , the original statement must be .

If a polygon is a triangle, then it has exactly three sides

Since as have been presented above, the contraposition is true, the original statement must be true

Step-by-step explanation:

The contrapositive statement; If a polygon has more than three sides, then it is not a triangle

We have that the definition of a triangle = A polygon with exactly three sides

Therefore;

A polygon with more than three sides is not a triangle and has (n - 1)/2×180 degrees interior angle, where n = The number of sides

Therefore, when n > 3, (n - 2)/2×180 > 180°

The sum of interior angles of a triangle = 180°

Therefore, the contrapositive statement, if a polygon has more than three sides, then it is not a triangle is true

Therefore, we have;

If a polygon is a triangle, then it has exactly three sides

Since as have been presented above, the contraposition is true, the original statement must be true

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