Question

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in the square pyramid shown below, which lines are parallel?

Explanation:

Step1: Recall the property of parallel lines

Parallel lines are lines in a plane that do not intersect. In a square pyramid, the base is a square. In a square, opposite sides are parallel.

Step2: Analyze each option

• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{EH}\): These lines intersect at point \(H\), so they are not parallel.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{FI}\): These lines intersect at point \(I\), so they are not parallel.
• For \(\overleftrightarrow{FI}\) and \(\overleftrightarrow{GH}\): Since the base \(FGHI\) is a square (assuming the base of the square - pyramid is \(FGHI\)), in a square \(FGHI\), \(FI\parallel GH\) (opposite sides of a square are parallel).
• For \(\overleftrightarrow{EG}\) and \(\overleftrightarrow{EH}\): These lines intersect at point \(E\), so they are not parallel.

Answer:

\(\overleftrightarrow{FI}\) and \(\overleftrightarrow{GH}\)