Question

1. using the diagram below, describe the relationship as parallel, intersecting, or skew.

a) $overline{ab}$ and $overline{bc}$ _____
b) $overline{ae}$ and $overline{bf}$ _____
c) $overline{ef}$ and $overline{ad}$ _____
d) plane $abc$ and plane $abf$ _____
e) plane $aed$ and plane $bfc$ _____

Explanation:

Step1: Recall line - line relationship definitions

Parallel lines are in the same plane and never intersect. Intersecting lines meet at a point. Skew lines are not in the same plane and do not intersect. Planes are parallel if they do not intersect and intersecting if they meet at a line.

Step2: Analyze $\overline{AB}$ and $\overline{BC}$

They share a common point $B$, so they are intersecting.

Step3: Analyze $\overline{AE}$ and $\overline{BF}$

They are in the same plane (the lateral - face plane of the prism - like shape) and do not intersect, so they are parallel.

Step4: Analyze $\overline{EF}$ and $\overline{AD}$

They are not in the same plane and do not intersect, so they are skew.

Step5: Analyze plane $ABC$ and plane $ABF$

They share the line $\overline{AB}$, so they are intersecting.

Step6: Analyze plane $AED$ and plane $BFC$

They do not intersect, so they are parallel.

Answer:

a) Intersecting
b) Parallel
c) Skew
d) Intersecting
e) Parallel