Question

Which lines are parallel in the square pyramid?

Select each correct answer.

​​​ BC←→ ​ and DE←→

CD←→ and BE←→

​ AD←→ ​ and ​​ ​ BC←→ ​

AB←→ and AD←→

Answer 1

Answer: The correct options are

(A) BC←→ ​and DE←→

(B) CD←→ and BE←→

Step-by-step explanation: We are given to select each pair of sides that are parallel to each other in the square pyramid.

We know that

the base of a square pyramid is a square. And the opposite sides of a square are parallel to each other.

So, in the given square pyramid ABCDE, the base is a square BCDE.

Therefore, the pair of parallel sides are

BC and DE ; CD and BE.

This implies that option (A) and (B) are correct.

Thus, the correct options are (A) and (B).

Answer 2

A square pyramid is a pyramid with a square base. In this problem, this base is formed by the points B, C, D and E as illustrated in the Figure above. So, the correct answers are:

First. (BC←→ ​ and DE←→)

This is indicated in Figure 1. As you can see, the red lines are parallel, that is:

`\overline{BC} \ is \ parallel \ to \ \overline{DE}`

Recall that two lines are parallel if they are always the same distant apart in which case they are equidistant, that is, they never meet.

Second. (CD←→ and BE←→)

This is indicated in Figure 2. As you can see, the green lines are parallel, that is:

`\overline{CD} \ is \ parallel \ to \ \overline{BE}`