Question

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 _____.

Answer 1

Contrapositive: if a polygon does not have more than 3 sides, then it is a triangle. Since it is a true statement, the contrapositive is a true statement, the original statement must be a true statement.

Explanation:

Original statement: if a polygon has more than three sides, then it is not a triangle.

Let P = a polygon has more than three sides

Let Q = it is not a triangle

Conditional statement: If P, then Q

Contrapositive statement: if not P, then not Q.

If a conditional statement is true, then the contrapositive is true.

If a contrapositive statement is true, then the contrapositive is true