Question

use the pyramid to complete parts (a) through (f) below.
d. which pair of lines are skew lines?
a. ( overleftrightarrow{ab} ) and ( overleftrightarrow{cd} )
b. ( overleftrightarrow{cd} ) and ( overleftrightarrow{be} )
c. ( overleftrightarrow{be} ) and ( overleftrightarrow{ae} )
d. ( overleftrightarrow{ad} ) and ( overleftrightarrow{bc} )

Explanation:

Step1: Recall Skew Lines Definition

Skew lines are non - parallel, non - intersecting, and lie in different planes.

Step2: Analyze Option A (AB and CD)

In the pyramid, AB and CD: If we consider the base (assuming a base like BCDE or similar, but from the diagram, AB and CD - let's check their relationship. Wait, maybe AB and CD are in the same plane? No, wait, let's check each option.

Step3: Analyze Option B (CD and BE)

CD and BE: Let's see the positions. CD is a line, BE is another line. Do they intersect? No. Are they parallel? No. And they lie in different planes. Wait, maybe not. Wait, let's check other options.

Step4: Analyze Option C (BE and AE)

BE and AE: These two lines intersect at point E, so they are not skew.

Step5: Analyze Option D (AD and BC)

AD and BC: Wait, no, let's re - check. Wait, the correct approach: Skew lines don't intersect and aren't parallel. Let's look at the pyramid structure. Let's assume the base is a quadrilateral (maybe BCDE) and the apex is A. So, CD and BE: Wait, maybe the correct pair is CD and BE? Wait, no, let's think again. Wait, the option B is CD and BE. Wait, let's check each pair:

• Option A: AB and CD. Are they parallel? Maybe in a pyramid with a rectangular base? If the base is a rectangle, AB and CD would be parallel. So they are not skew.
• Option B: CD and BE. CD is a side of the base, BE is a line from B to E (apex - related? No, E is a vertex? Wait, the diagram has A, B, C, D, E. So CD and BE: Do they intersect? No. Are they parallel? No. So they are skew.
• Option C: BE and AE. They intersect at E, so not skew.
• Option D: AD and BC. Maybe they intersect or are parallel? No, wait, maybe not. Wait, the key is that skew lines are non - intersecting, non - parallel, different planes. So CD and BE (Option B) are skew.

Answer:

B. $\overleftrightarrow{CD}$ and $\overleftrightarrow{BE}$