Question

7 multiple choice 5 points given the figure as marked, which segment must be an altitude of \\( \triangle a b c \\)?

Explanation:

Step1: Recall the definition of an altitude

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Step2: Analyze each segment

• For \(\overline{CF}\): It is a perpendicular segment from vertex \(C\) to side \(AB\).
• For \(\overline{DC}\): It is not a segment from a vertex of \(\triangle ABC\) to the line containing the opposite side.
• For \(\overline{BE}\): It is not a segment from a vertex of \(\triangle ABC\) to the line containing the opposite side.
• For \(\overline{CE}\): It is not a segment from a vertex of \(\triangle ABC\) to the line containing the opposite side.

Answer:

\(\overline{CF}\)