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. $overleftrightarrow{ae}$ and $overleftrightarrow{cd}$
b. $overleftrightarrow{ad}$ and $overleftrightarrow{bc}$
c. $overleftrightarrow{cd}$ and $overleftrightarrow{be}$
d. $overleftrightarrow{bc}$ and $overleftrightarrow{cd}$
f. find a plane not determined by one of the triangular faces or by the base. choose the correct answer below.
a. aec
b. bad
c. aeb
d. ced

Explanation:

Step1: Recall parallel - line concept

In a three - dimensional figure, parallel lines are lines that do not intersect and lie in the same plane (or in parallel planes). In a pyramid, we check the position of each pair of lines.
For option A, AE and CD are not parallel as AE is an edge connecting the apex to a base - vertex and CD is a base - edge.
For option B, AD and BC are parallel because in the base of the pyramid (assuming the base is a quadrilateral), if the base is a parallelogram (a common case for pyramids with quadrilateral bases), opposite sides of the base are parallel.
For option C, CD and BE are not parallel as they are in different non - parallel planes.
For option D, BC and CD are adjacent sides of the base, so they are not parallel.

Step2: Recall plane - determination concept

The triangular faces of the pyramid are ADE, CDE, ABE, BCE. The base is ABCD.
For option A, AEC is a triangular face.
For option B, BAD is not a triangular face and not the base. It is a plane formed by three non - collinear points that is not one of the main triangular faces or the base.
For option C, AEB is a triangular face.
For option D, CED is a triangular face.

Answer:

e. B. AD and BC
f. B. BAD