Question

what are the opposite rays to \\( \overrightarrow { fg } \\)
select all correct options
\\( \overrightarrow { gf } \\)
\\( \overrightarrow { fe } \\)
\\( \overrightarrow { fd } \\)
\\( \overrightarrow { ed } \\)
\\( \overleftarrow { gd } \\)

Explanation:

Step1: Recall the definition of opposite rays

Opposite rays are two rays that have the same endpoint and form a straight line (i.e., the sum of their measures is \(180^{\circ}\)). The ray \(\overrightarrow{FG}\) has endpoint \(F\) and extends towards \(G\).

Step2: Analyze each option

• For \(\overrightarrow{GF}\): This is the same ray as \(\overrightarrow{FG}\) but with the arrow direction reversed. It is not an opposite ray.
• For \(\overrightarrow{FE}\): Rays \(\overrightarrow{FG}\) and \(\overrightarrow{FE}\) do not form a straight line.
• For \(\overrightarrow{FD}\): Rays \(\overrightarrow{FG}\) and \(\overrightarrow{FD}\) have the same endpoint \(F\) and form a straight line (since \(D\), \(E\), \(F\), \(G\) are colinear).
• For \(\overrightarrow{ED}\): The endpoint of \(\overrightarrow{ED}\) is \(E\), not \(F\), so it cannot be an opposite ray to \(\overrightarrow{FG}\) (which has endpoint \(F\)).
• For \(\overleftarrow{GD}\): The endpoint of \(\overleftarrow{GD}\) is \(G\), not \(F\), so it cannot be an opposite ray to \(\overrightarrow{FG}\) (which has endpoint \(F\)).

Answer:

\(\overrightarrow{FD}\)