Medians, Altitudes, Orthocenters, & Centroids

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

What is the relationship between the centroid and the lengths of the segments created by the medians?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

If a median is drawn in a triangle, what is the ratio of the lengths of the segments it creates?

Back

The median divides the triangle into two smaller triangles of equal area.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

How many altitudes does a triangle have?

Back

A triangle has three altitudes, one from each vertex.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

What is the relationship between the orthocenter and the type of triangle?

Back

The orthocenter's position varies based on the type of triangle: it is inside for acute triangles, on the vertex for right triangles, and outside for obtuse triangles.

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is a perpendicular segment from a vertex to the opposite side.