Question

lines cm, hl, en and ab are shown where (mangle cde = 90^{circ}). determine if the given conditions could be used to justify that (overline{en}paralleloverline{ab}). condition is (overline{en}paralleloverline{ab})? justification (angle cdjcongangle dlk) choose your answer answer (angle almcongangle dlk) choose your answer answer (angle edccongangle klm) choose your answer answer

Explanation:

Step1: Recall parallel - line criteria

If two lines are cut by a transversal, corresponding angles are congruent, then the lines are parallel; if alternate - interior angles are congruent, then the lines are parallel; if alternate - exterior angles are congruent, then the lines are parallel.

Step2: Analyze $\angle CDJ\cong\angle DLK$

$\angle CDJ$ and $\angle DLK$ are alternate - interior angles. If $\angle CDJ\cong\angle DLK$, by the alternate - interior angles postulate, $\overline{EN}\parallel\overline{AB}$.

Step3: Analyze $\angle ALM\cong\angle DLK$

$\angle ALM$ and $\angle DLK$ are vertical angles. Vertical - angle congruence does not directly imply that $\overline{EN}\parallel\overline{AB}$. There is no parallel - line postulate or theorem that uses vertical - angle congruence to prove parallel lines.

Step4: Analyze $\angle EDC\cong\angle KLM$

$\angle EDC$ and $\angle KLM$ have no relation (such as corresponding, alternate - interior, or alternate - exterior) with respect to the lines $\overline{EN}$ and $\overline{AB}$ that would imply parallelism.

Answer:

Condition	Is $\overline{EN}\parallel\overline{AB}$?	Justification
$\angle ALM\cong\angle DLK$	No	Vertical - angle congruence does not imply parallelism
$\angle EDC\cong\angle KLM$	No	No relevant parallel - line relation