Question

Can an altitude coincide with a median in an isosceles triangle?

Answer 1

Answer:

Step-by-step explanation:

In an isosceles triangle, the altitude and median are the same line segment when drawn from the vertex opposite the base to the base.

We need to be familiar with a couple definitions.

Altitude of a triangle: A line segment drawn from a vertex of a triangle to the side opposite that vertex, such that the line segment is perpendicular (forms a right angle with) that opposite side.Median of a triangle: A line segment drawn from a vertex of a triangle to the side opposite that vertex, such that the line segment intersects the opposite side at its midpoint.

In an isosceles triangle, the two sides that are equal meet at a vertex, call it vertex A, that lies directly above the midpoint of the base. Because of this, the altitude that runs from A to the base intersects the base at its midpoint, making it the median from A to the base as well.

Therefore, in an isosceles triangle, the altitude and median are the same line segment when drawn from the vertex opposite the base to the base.