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 $\overleftrightarrow{bc}$
e. find a pair of distinct parallel lines. choose the correct answer below.
a. $\overleftrightarrow{cd}$ and $\overleftrightarrow{de}$
b. $\overleftrightarrow{cd}$ and $\overleftrightarrow{be}$
c. $\overleftrightarrow{ae}$ and $\overleftrightarrow{cd}$
d. $\overleftrightarrow{ad}$ and $\overleftrightarrow{bc}$

1. find a plane not determined by one of the triangular faces or by the base. choose the correct answer below.

Explanation:

Step1: Recall Skew Lines Definition

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

Step2: Analyze Each Option

• Option A: $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$: In the pyramid, $AB$ and $CD$ may be in related planes or intersect (depending on the pyramid structure, but generally, they are not skew as they might be in a way that they are not skew).
• Option B: $\overleftrightarrow{CD}$ and $\overleftrightarrow{BE}$: $CD$ and $BE$: Let's consider the planes. $CD$ is in one set of planes (maybe the base - related or a lateral face - related) and $BE$ is in another. They do not intersect and are not parallel.
• Option C: $\overleftrightarrow{BE}$ and $\overleftrightarrow{AE}$: $BE$ and $AE$ intersect at point $E$, so they are not skew.
• Option D: $\overleftrightarrow{AD}$ and $\overleftrightarrow{BC}$: Depending on the pyramid structure, these may not be skew.

After analyzing the definitions and the structure of the pyramid (from the diagram), the pair of skew lines is $\overleftrightarrow{CD}$ and $\overleftrightarrow{BE}$.

Answer:

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