Question

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which pairs of lines are perpendicular to each other? select all that apply.
□ a) $overleftrightarrow{fc}$ and $overleftrightarrow{bg}$
□ b) $overleftrightarrow{ae}$ and $overleftrightarrow{fc}$
□ c) $overleftrightarrow{dg}$ and $overleftrightarrow{bg}$
□ d) $overleftrightarrow{cg}$ and $overleftrightarrow{fg}$
□ e) $overleftrightarrow{ag}$ and $overleftrightarrow{eg}$

Explanation:

Step1: Recall Perpendicular Definition

Perpendicular lines form a \(90^\circ\) (right) angle. We check each option by observing the diagram (right angle symbol at \( \angle FGE\) and other angles).

Step2: Analyze Option A (\(\overleftrightarrow{FC}\) and \(\overleftrightarrow{BG}\))

\(\overleftrightarrow{FC}\) is horizontal, \(\overleftrightarrow{BG}\) is a slant line. No right angle between them. So not perpendicular.

Step3: Analyze Option B (\(\overleftrightarrow{AE}\) and \(\overleftrightarrow{FC}\))

\(\overleftrightarrow{AE}\) is vertical, \(\overleftrightarrow{FC}\) is horizontal. Vertical and horizontal lines are perpendicular (form \(90^\circ\) angle). So this pair is perpendicular.

Step4: Analyze Option C (\(\overleftrightarrow{DG}\) and \(\overleftrightarrow{BG}\))

\(\overleftrightarrow{DG}\) and \(\overleftrightarrow{BG}\) form a right angle (from diagram, as \( \angle BGD\) looks like \(90^\circ\) with the right angle symbol's symmetry). So this pair is perpendicular.

Step5: Analyze Option D (\(\overleftrightarrow{CG}\) and \(\overleftrightarrow{FG}\))

\(\overleftrightarrow{CG}\) and \(\overleftrightarrow{FG}\) are a straight line (opposite rays), so they form a \(180^\circ\) angle, not \(90^\circ\). Not perpendicular.

Step6: Analyze Option E (\(\overleftrightarrow{AG}\) and \(\overleftrightarrow{EG}\))

\(\overleftrightarrow{AG}\) and \(\overleftrightarrow{EG}\) are a straight line (opposite rays), forming \(180^\circ\) angle, not \(90^\circ\). Not perpendicular.

Answer:

B. \(\overleftrightarrow{AE}\) and \(\overleftrightarrow{FC}\), C. \(\overleftrightarrow{DG}\) and \(\overleftrightarrow{BG}\)