Question

question 28

any altitude of an equilateral triangle is also a median of the triangle.

true
false

Explanation:

Analyze equilateral triangle properties

In an equilateral triangle, all three sides are equal in length, and all three interior angles are equal to \(60^\circ\).

Examine the relationship between altitude and median

An altitude is a segment from a vertex perpendicular to the opposite side. A median is a segment from a vertex to the midpoint of the opposite side. For any vertex of an equilateral triangle, the altitude drawn to the opposite side bisects that side (due to symmetry and triangle congruence, such as HL congruence). Therefore, the altitude also connects the vertex to the midpoint of the opposite side, making it a median.

Evaluate the statement

Since every altitude in an equilateral triangle bisects the opposite side, any altitude of an equilateral triangle is indeed also a median of the triangle. The statement is True.

Answer:

• True (Correct answer)
• False