Question

What kind of triangle has three angle bisectors that are also altitudes and medians?

Short answer

Equilateral triangle has three angle bisectors that are also altitudes and medians

Step-by-step solution

Step 1. Definition of angle bisectors.

Angle Bisector is a line segment joining a vertex of a triangle with the opposite side such that the angle at the vertex is split into two equal parts.

Step 2. Definition of altitude.

Altitude is a line segment joining a vertex of a triangle with the opposite side such that the segment is perpendicular to the opposite side.

Step 3. Definition of median.

Median is a line segment joining a vertex of the triangle with the midpoint of the opposite side.

Step 4. Draw and name a triangle that has three angle bisectors that are also altitudes and medians

In an equilateral triangle all three lines are all types that is each angle bisector is also an altitude as well as a median.

Thus, equilateral triangle is the required triangle.