Question

use the pyramid to complete parts (a) through (f) below.
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}
f. find a plane not determined by one of the triangular faces or by the base. choose the correct answer below.
a. bed
b. ced
c. aeb
d. bad

Explanation:

Part (e)

Step1: Analyze Option A

Lines \( \overleftrightarrow{CD} \) and \( \overleftrightarrow{DE} \) meet at \( D \), so they are not parallel.

Step2: Analyze Option B

Lines \( \overleftrightarrow{CD} \) and \( \overleftrightarrow{BE} \): \( CD \) is in the base, \( BE \) is a lateral edge; they are not parallel.

Step3: Analyze Option C

Lines \( \overleftrightarrow{AE} \) and \( \overleftrightarrow{CD} \): \( AE \) is a lateral edge, \( CD \) is a base edge; they are not parallel.

Step4: Analyze Option D

In the base (a parallelogram, since \( ABCD \) is the base of the pyramid), \( AD \parallel BC \) (opposite sides of a parallelogram are parallel). So \( \overleftrightarrow{AD} \) and \( \overleftrightarrow{BC} \) are parallel.

Step1: Analyze Option A

Plane \( BED \): \( BED \) is a triangular face? No, the triangular faces are \( AEB, BEC, CED, DEA \). \( BED \) is not a standard triangular face or the base (base is \( ABCD \)). Wait, let's check others.

Step2: Analyze Option B

Plane \( CED \): \( CED \) is a triangular face (lateral face with vertex \( E \) and base \( CD \)).

Step3: Analyze Option C

Plane \( AEB \): \( AEB \) is a triangular face (lateral face with vertex \( E \) and base \( AB \)).

Step4: Analyze Option D

Plane \( BAD \): \( BAD \) is part of the base \( ABCD \) (a triangular part of the base parallelogram).

Wait, re - evaluating: The base is \( ABCD \) (a quadrilateral, likely a parallelogram). The triangular faces are \( AEB, BEC, CED, DEA \). Plane \( BED \): Let's see the points \( B, E, D \). \( B \) and \( D \) are base vertices, \( E \) is the apex. This plane is not one of the four triangular faces (which have bases \( AB, BC, CD, DA \)) and not the base \( ABCD \). Plane \( CED \) is a triangular face (base \( CD \)), \( AEB \) is a triangular face (base \( AB \)), \( BAD \) is part of the base. So \( BED \) is the plane not determined by a triangular face or the base.

Answer:

D. \( \overleftrightarrow{AD} \) and \( \overleftrightarrow{BC} \)

Part (f)