Question

for 16 - 17, determine whether $overleftrightarrow{jk} parallel overleftrightarrow{nm}$

1. $jn = 18$, $jl = 30$, $km = 21$, and $ml = 35$.

yes or no

1. $km = 24$, $kl = 44$, and $nl = \frac{5}{6}jn$.

yes or no

Explanation:

Problem 16:

Step1: Find $NL$

$NL = JL - JN = 30 - 18 = 12$

Step2: Check proportional segments

We use the Converse of the Triangle Proportionality Theorem: if $\frac{JN}{NL} = \frac{KM}{ML}$, then $\overline{JK} \parallel \overline{NM}$.
Calculate $\frac{JN}{NL} = \frac{18}{12} = \frac{3}{2}$
Calculate $\frac{KM}{ML} = \frac{21}{35} = \frac{3}{5}$
Since $\frac{3}{2}
eq \frac{3}{5}$, the segments are not parallel.

Problem 17:

Step1: Find $ML$

$ML = KL - KM = 44 - 24 = 20$

Step2: Express $JL$ in terms of $JN$

$JL = JN + NL = JN + \frac{5}{6}JN = \frac{11}{6}JN$

Step3: Check proportional segments

Calculate $\frac{JN}{JL} = \frac{JN}{\frac{11}{6}JN} = \frac{6}{11}$
Calculate $\frac{KM}{KL} = \frac{24}{44} = \frac{6}{11}$
Since $\frac{JN}{JL} = \frac{KM}{KL}$, by the Converse of the Triangle Proportionality Theorem, the segments are parallel.

Answer:

1. no
2. yes