Question

given the figure below, which segments are altitudes? (hint: there are 3 correct answers!)

Explanation:

Step1: Recall the definition of 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 \(\overline{AF}\): It is a perpendicular segment from vertex \(A\) to the line containing side \(BC\).
• For \(\overline{CD}\): It is a perpendicular segment from vertex \(C\) to the line containing side \(AB\).
• For \(\overline{BG}\): It is a perpendicular segment from vertex \(B\) to the line containing side \(AC\).
• \(\overline{EC}\) is not an altitude as it is not perpendicular to the opposite side.
• \(\overline{AC}\) is a side of the triangle, not an altitude.
• \(\overline{AD}\) is not perpendicular to the opposite side (it is part of side \(AB\) in a non - perpendicular way here).
• \(\overline{BC}\) is a side of the triangle, not an altitude.

Answer:

\(\overline{AF}\), \(\overline{CD}\), \(\overline{BG}\)