Question

if \\(jklm\\) is a trapezoid, which statements must be true? check all that apply.

a. \\(\angle j\\) is congruent to \\(\angle k\\).
b. \\(\overline{jk}\\) is parallel to \\(\overline{lm}\\).
c. \\(\angle j\\) is supplementary to \\(\angle k\\).
d. \\(\overline{jk} \cong \overline{lm}\\)
e. \\(\overline{jm} \cong \overline{kl}\\)
f. \\(\overline{kl}\\) is parallel to \\(\overline{jm}\\).

Explanation:

Identify parallel bases of the trapezoid

$$ \overline{KL} \parallel \overline{JM} $$

Analyze consecutive interior angles

$$ m\angle J + m\angle K = 180^\circ \implies \angle J \text{ is supplementary to } \angle K $$

Evaluate other options

$$
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Answer:

• A. \(\angle J\) is congruent to \(\angle K\).
• B. \(\overline{JK}\) is parallel to \(\overline{LM}\).
• C. \(\angle J\) is supplementary to \(\angle K\). (Correct answer)
• D. \(\overline{JK} \cong \overline{LM}\)
• E. \(\overline{JM} \cong \overline{KL}\)
• F. \(\overline{KL}\) is parallel to \(\overline{JM}\). (Correct answer)