Question

lines cm, hl, en and ab are shown where m∠cde = 90°. determine if the given conditions could be used to justify that (overline{en}paralleloverline{ab}). condition is (overline{en}paralleloverline{ab})? justification ∠cdj≅∠dlk choose your answer answer ∠alm≅∠dlk choose your answer answer ∠edc≅∠klm choose your answer answer

Explanation:

Step1: Recall parallel - line theorems

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

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

$\angle CDJ$ and $\angle DLK$ are alternate - interior angles formed by lines $EN$ and $AB$ with transversal $HL$. If $\angle CDJ\cong\angle DLK$, then by the Alternate - Interior Angles Theorem, $\overline{EN}\parallel\overline{AB}$.

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

$\angle ALM$ and $\angle DLK$ are vertical angles. Vertical - angle congruence does not imply that $\overline{EN}\parallel\overline{AB}$. There is no parallel - line relationship based on vertical - angle congruence.

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

$\angle EDC$ and $\angle KLM$ have no direct relationship (such as corresponding, alternate - interior, or alternate - exterior) with respect to lines $EN$ and $AB$ and a transversal. So, $\angle EDC\cong\angle KLM$ cannot be used to justify $\overline{EN}\parallel\overline{AB}$.

Answer:

• For $\angle CDJ\cong\angle DLK$: Yes, by the Alternate - Interior Angles Theorem
• For $\angle ALM\cong\angle DLK$: No, vertical - angle congruence does not imply parallel lines
• For $\angle EDC\cong\angle KLM$: No, no relevant parallel - line relationship