To disprove the statement "If the polygon is a quadrilateral, then it has two pairs of congruent sides," we can provide a counterexample using a trapezoid.
A trapezoid is a type of quadrilateral that has only one pair of parallel sides. It does not necessarily have two pairs of congruent sides. For example, consider a trapezoid with sides of lengths 5, 10, 4, and 7. In this case, there is only one pair of congruent sides (none in this specific example) and the conditions of the statement do not hold true.
Thus, the trapezoid serves as a counterexample, demonstrating that not all quadrilaterals have two pairs of congruent sides.
1 answer