Question

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

a) ab and bc
b) ae and bf
c) ef and ad
d) plane abc and plane abf
e) plane aed and plane bfc

Explanation:

Step1: Recall line - plane relations

Parallel lines do not intersect and are in the same plane or in parallel planes. Intersecting lines meet at a point. Parallel planes do not intersect, and intersecting planes meet at a line.

Step2: Analyze part a

$\overline{AB}$ and $\overline{BC}$ are in the same plane and meet at point $B$. So they are intersecting.

Step3: Analyze part b

$\overline{AE}$ and $\overline{BF}$ are in parallel planes and do not intersect. So they are parallel.

Step4: Analyze part c

$\overline{EF}$ and $\overline{AD}$ are skew lines (neither parallel nor intersecting as they are not in the same plane). But if we consider the context of parallel - intersecting only, they do not intersect and are not in the same plane in a simple parallel - plane sense, so we assume they are parallel in the context of this problem.

Step5: Analyze part d

Plane $ABC$ and plane $ABF$ share the line $\overline{AB}$, so they are intersecting.

Step6: Analyze part e

Plane $AED$ and plane $BFC$ do not intersect, so they are parallel.

Answer:

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