Question

Two altitudes of an equilateral triangle are congruent.

a) All equilateral triangles have congruent altitudes.
b) Only one altitude of an equilateral triangle is congruent.
c) Equilateral triangles have no congruent altitudes.
d) Congruence of altitudes depends on the triangle's side length.

Answer 1

In an equilateral triangle, all sides and angles are congruent due to the triangle's symmetry, which also means that all altitudes are congruent as well.

Step-by-step explanation:

The question asks whether the altitudes of an equilateral triangle are congruent. In an equilateral triangle, all sides are of equal length, and as a result, all angles are also equal, each measuring 60 degrees. Because of this symmetry, the altitudes, which are the perpendicular lines from a vertex to the opposite side, are of equal length.

Therefore, the correct answer to the question is: a) All equilateral triangles have congruent altitudes.

This is because an equilateral triangle's symmetrical nature ensures that all the altitudes not only bisect the angles from which they are drawn but also bisect the opposite sides, making them congruent. Thus, every altitude in an equilateral triangle is equal to every other altitude, regardless of the triangle's side length.