Question

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the figure shown is a rectangular prism.
which edges are parallel to \\( \overline { b d } \\) ?
select each correct answer.
\\( \square \overline { m k } \\)
\\( \square \overline { y h } \\)
\\( \square \overline { b m } \\)
\\( \square \overline { a h } \\)
\\( \square \overline { p y } \\)

Explanation:

Step1: Recall the properties of a rectangular prism

In a rectangular prism, opposite edges are parallel.

Step2: Analyze each option

• For \(\overline{MK}\): In a rectangular prism, \(BD\) and \(MK\) are opposite edges of the top - bottom parallel faces. So \(BD\parallel MK\).
• For \(\overline{YH}\): \(BD\) and \(YH\) are not opposite edges in a way that satisfies the parallel condition.
• For \(\overline{BM}\): \(BD\) and \(BM\) are adjacent edges, not parallel.
• For \(\overline{AH}\): \(BD\) and \(AH\) are not opposite edges in a way that satisfies the parallel condition.
• For \(\overline{PY}\): \(BD\) and \(PY\) are opposite edges of the front - back parallel faces. So \(BD\parallel PY\).

Answer:

\(\overline{MK}\), \(\overline{PY}\)