2. $\overline{cm}$, $\overline{hi}$, $\overline{en}$, and $\overline{ab}$ are shown where $\angle lki = 94^\circ$.

determine if the given conditions could be used to justify that $\overline{en} \parallel \overline{ab}$ or $\overline{cm} \parallel \overline{hi}$. then justify your answer.

| condition | is $\overline{en} \parallel \overline{ab}$ or $\overline{cm} \parallel \overline{hi}$? | justification |
| --- | --- | --- |
| $\angle cdj \cong \angle klm$ | $\circ$ yes $\circ$ no | |
| $\angle cde \cong \angle mla$ | $\circ$ yes $\circ$ no | |
| $m\angle edl + m\angle njk = 180^\circ$ | $\circ$ yes $\circ$ no | |
| $\angle klm \cong \angle hjn$ | $\circ$ yes $\circ$ no | |
| $\angle jkl \cong \angle bki$ | $\circ$ yes $\circ$ no | |
| if $\angle bki = 86^\circ$, then $m\angle bki + m\angle lki = 180^\circ$ | $\circ$ yes $\circ$ no | |

Question

2. $\overline{cm}$, $\overline{hi}$, $\overline{en}$, and $\overline{ab}$ are shown where $\angle lki = 94^\circ$.

determine if the given conditions could be used to justify that $\overline{en} \parallel \overline{ab}$ or $\overline{cm} \parallel \overline{hi}$. then justify your answer.

| condition | is $\overline{en} \parallel \overline{ab}$ or $\overline{cm} \parallel \overline{hi}$? | justification |
| --- | --- | --- |
| $\angle cdj \cong \angle klm$ | $\circ$ yes $\circ$ no |  |
| $\angle cde \cong \angle mla$ | $\circ$ yes $\circ$ no |  |
| $m\angle edl + m\angle njk = 180^\circ$ | $\circ$ yes $\circ$ no |  |
| $\angle klm \cong \angle hjn$ | $\circ$ yes $\circ$ no |  |
| $\angle jkl \cong \angle bki$ | $\circ$ yes $\circ$ no |  |
| if $\angle bki = 86^\circ$, then $m\angle bki + m\angle lki = 180^\circ$ | $\circ$ yes $\circ$ no |  |

Accepted Answer

# Explanation:
## Step1: Analyze $\angle CDJ\cong\angle KLM$
These angles are not corresponding, alternate - interior, or same - side interior angles for either $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.
## Step2: Analyze $\angle CDE\cong\angle MLA$
These angles are not corresponding, alternate - interior, or same - side interior angles for either $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.
## Step3: Analyze $m\angle EDL + m\angle NJK=180^{\circ}$
These angles are not corresponding, alternate - interior, or same - side interior angles for either $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.
## Step4: Analyze $\angle KLM\cong\angle HJN$
These angles are not corresponding, alternate - interior, or same - side interior angles for either $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.
## Step5: Analyze $\angle JKL\cong\angle BKI$
These angles are vertical angles and have no relation to proving $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.
## Step6: Analyze If $\angle BKI = 86^{\circ}$, then $m\angle BKI+m\angle LKI = 180^{\circ}$
This is just a linear - pair relationship ($\angle BKI$ and $\angle LKI$ are adjacent and form a straight line), and  has no relation to proving $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$. So, the answer is No.

# Answer:
| Condition | Is $\overline{EN}\parallel\overline{AB}$ or $\overline{CM}\parallel\overline{HI}$? | Justification |
|---|---|---|
|$\angle CDJ\cong\angle KLM$| No | Not corresponding, alternate - interior, or same - side interior angles |
|$\angle CDE\cong\angle MLA$| No | Not corresponding, alternate - interior, or same - side interior angles |
|$m\angle EDL + m\angle NJK = 180^{\circ}$| No | Not corresponding, alternate - interior, or same - side interior angles |
|$\angle KLM\cong\angle HJN$| No | Not corresponding, alternate - interior, or same - side interior angles |
|$\angle JKL\cong\angle BKI$| No | Vertical angles, no parallel - line relation |
|If $\angle BKI = 86^{\circ}$, then $m\angle BKI+m\angle LKI = 180^{\circ}$| No | Linear - pair (adjacent angles on a straight line), no parallel - line relation |

condition	is \\(\overline{en} \parallel \overline{ab}\\) or \\(\overline{cm} \parallel \overline{hi}\\)?	justification
\\(\angle cde \cong \angle mla\\)	\\(\circ\\) yes \\(\circ\\) no
\\(m\angle edl + m\angle njk = 180^\circ\\)	\\(\circ\\) yes \\(\circ\\) no
\\(\angle klm \cong \angle hjn\\)	\\(\circ\\) yes \\(\circ\\) no
\\(\angle jkl \cong \angle bki\\)	\\(\circ\\) yes \\(\circ\\) no
if \\(\angle bki = 86^\circ\\), then \\(m\angle bki + m\angle lki = 180^\circ\\)	\\(\circ\\) yes \\(\circ\\) no

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze \(\angle CDJ\cong\angle KLM\)

Step2: Analyze \(\angle CDE\cong\angle MLA\)

Step3: Analyze \(m\angle EDL + m\angle NJK=180^{\circ}\)

Step4: Analyze \(\angle KLM\cong\angle HJN\)

Step5: Analyze \(\angle JKL\cong\angle BKI\)

Step6: Analyze If \(\angle BKI = 86^{\circ}\), then \(m\angle BKI+m\angle LKI = 180^{\circ}\)

Answer:

Condition	Is \(\overline{EN}\parallel\overline{AB}\) or \(\overline{CM}\parallel\overline{HI}\)?	Justification
\(\angle CDE\cong\angle MLA\)	No	Not corresponding, alternate - interior, or same - side interior angles
\(m\angle EDL + m\angle NJK = 180^{\circ}\)	No	Not corresponding, alternate - interior, or same - side interior angles
\(\angle KLM\cong\angle HJN\)	No	Not corresponding, alternate - interior, or same - side interior angles
\(\angle JKL\cong\angle BKI\)	No	Vertical angles, no parallel - line relation
If \(\angle BKI = 86^{\circ}\), then \(m\angle BKI+m\angle LKI = 180^{\circ}\)	No	Linear - pair (adjacent angles on a straight line), no parallel - line relation