Question

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select parallel or not parallel for each set of given information.
segment lengths parallel not parallel
$ad = 2, db = 4, ce = 3, eb = 6$ $circ$ $circ$
$ad = 2, db = 3, ce = 6, eb = 9$ $circ$ $circ$
$ad = 2, db = 5, ce = 4, eb = 7$ - -

Explanation:

Step1: Check ratio for first case

Calculate $\frac{AD}{DB}$ and $\frac{CE}{EB}$.
$\frac{AD}{DB}=\frac{2}{4}=\frac{1}{2}$, $\frac{CE}{EB}=\frac{3}{6}=\frac{1}{2}$

Step2: Check ratio for second case

Calculate $\frac{AD}{DB}$ and $\frac{CE}{EB}$.
$\frac{AD}{DB}=\frac{2}{3}$, $\frac{CE}{EB}=\frac{6}{9}=\frac{2}{3}$

Step3: Check ratio for third case

Calculate $\frac{AD}{DB}$ and $\frac{CE}{EB}$.
$\frac{AD}{DB}=\frac{2}{5}$, $\frac{CE}{EB}=\frac{4}{7}$

Answer:

1. For $AD=2, DB=4, CE=3, EB=6$: Parallel
2. For $AD=2, DB=3, CE=6, EB=9$: Parallel
3. For $AD=2, DB=5, CE=4, EB=7$: Not parallel