Question

the figure shown is a rectangular prism. which edges are parallel to $overline{bd}$? select each correct answer. $overline{yh}$ $overline{mk}$ $overline{bm}$ $overline{py}$ $overline{ah}$

Explanation:

Step1: Recall parallel - edge property in rectangular prism

In a rectangular prism, parallel edges are those that do not intersect and have the same direction.

Step2: Analyze the position of \(\overline{BD}\)

\(\overline{BD}\) is a diagonal - like edge in the rectangular prism. Edges that are parallel to it will have the same 3 - D orientation.

Step3: Check each option

For \(\overline{YH}\), it has the same orientation as \(\overline{BD}\) in the 3 - D space of the rectangular prism. They are parallel.
For \(\overline{MK}\), it also has the same orientation as \(\overline{BD}\) and is parallel to it.
\(\overline{BM}\), \(\overline{PY}\), and \(\overline{AH}\) do not have the same orientation as \(\overline{BD}\) and are not parallel to it.

Answer:

A. \(\overline{YH}\)
B. \(\overline{MK}\)