Question

assume that the set of given information is true. use the law of detachment to form a conclusion about the situation. if a quadrilateral has exactly one pair of parallel sides, then the quadrilateral is a trapezoid. the quadrilateral has exactly one pair of parallel sides. choose the correct conclusion below. a. all trapezoids are quadrilaterals. b. if a trapezoid has exactly one pair of parallel sides, then the trapezoid is a quadrilateral. c. the trapezoid is a quadrilateral. d. all quadrilaterals are trapezoids. e. the quadrilateral is a trapezoid.

Explanation:

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is true. Here, the conditional statement is "If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid". Given that the quadrilateral has exactly one pair of parallel sides (hypothesis is true), we can conclude it is a trapezoid.

Answer:

A. All trapezoids are quadrilaterals.
B. If a trapezoid has exactly one pair of parallel sides, then the trapezoid is a quadrilateral.
C. The trapezoid is a quadrilateral.
D. All quadrilaterals are trapezoids is incorrect as not all quadrilaterals have exactly one - pair of parallel sides.
E. Just saying the quadrilateral is a trapezoid without the proper logical build - up from the given information is not as comprehensive as using the properties and the law of detachment. The most correct conclusion based on the Law of Detachment and the definition of a trapezoid is that if a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid which is option B.