Question

if jklm is a trapezoid, which statements must be true? check all that apply. a. jk is perpendicular to kl. b. kl is parallel to jm. c. ∠j is congruent to ∠m. d. ∠j is congruent to ∠k. e. jk is parallel to lm. f. ∠j is supplementary to ∠k.

Explanation:

Step1: Recall trapezoid definition

A trapezoid has one - pair of parallel sides. In trapezoid \(JKLM\), assume \(JK\parallel LM\).

Step2: Analyze angle - side relationships

• Option A: There is no information to suggest that \(JK\) is perpendicular to \(KL\) in a general trapezoid.
• Option B: \(KL\) is not parallel to \(JM\) in a trapezoid (a trapezoid has only one pair of parallel sides).
• Option C: There is no reason for \(\angle J\) to be congruent to \(\angle M\) in a general trapezoid.
• Option D: There is no reason for \(\angle J\) to be congruent to \(\angle K\) in a general trapezoid.
• Option E: By the definition of a trapezoid, if \(JKLM\) is a trapezoid, then \(JK\) is parallel to \(LM\).
• Option F: In a trapezoid, adjacent angles along the non - parallel sides are supplementary. So \(\angle J\) and \(\angle K\) are supplementary.

Answer:

E. \(JK\) is parallel to \(LM\)
F. \(\angle J\) is supplementary to \(\angle K\)