Question

HELP ASAPThe figure shown is a rectangular prism.
Which edges are parallel to AH ?
Select each correct answer.

Answer 1

Answer:

Options A and C are correct.

Step-by-step explanation:

In the figure attached, a rectangular prism has been shown with an edge AH.

Parallel to this edge AH, side MK is parallel (Located on the plane AMKH of the prism).

Another side BD is also parallel to AH (Located on the diagonal plane ABDH)

Therefore, two sides BD and MK are parallel to the edge AH of the prism.

Options A and C are correct.

Answer 2

Two linear edges of the rectangular are parallel if they do not meet and have the same direction vectors

The correct options for the edges parallel to $\overline{AH}$ are $\mathbf{\overline{BD}}$ and $\mathbf{\overline{MK}}$

The reason for the above selection is as follows:

The edges of the given rectangular prism are;

Horizontal edges in the x-direction: $\overline{AH}$, $\overline{PY}$, $\overline{BD}$, $\overline{MK}$

Horizontal edges in the z-direction: $\overline{HK}$, $\overline{BP}$, $\overline{DY}$, $\overline{AM}$

Vertical edges: $\overline{AP}$, $\overline{BM}$, $\overline{DK}$, $\overline{HY}$

The required information:

The names of the edges that are parallel to $\overline{AH}$

Strategy:

Two edges are parallel if they are oriented in the same axial direction or have the same direction vectors

Solution:

The edged that are in the same axial direction as $\overline{AH}$ are $\overline{PY}$, $\overline{BD}$ and $\overline{MK}$

Therefore, the correct options from the options given for the edges of the rectangular prism parallel to $\overline{AH}$ are;

$\mathbf{\overline{BD}}$ and $\mathbf{\overline{MK}}$

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