Medians, Altitudes, Orthocenters, & Centroids

Front

What is an Altitude in a triangle?

Back

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

Front

What is a Median in a triangle?

Back

A median is a segment from a vertex of a triangle to the midpoint of the opposite side.

Front

What is a Centroid?

Back

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

Front

What is an Orthocenter?

Back

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

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the relationship between the centroid and 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

What is the measure of the angles formed by an altitude?

Back

An altitude forms a right angle (90°) with the side it intersects.

Front

If a median divides a triangle into two equal areas, what does this imply?

Back

It implies that the median splits the triangle into two triangles of equal area.

Front

What is the significance of the orthocenter in a triangle?

Back

The orthocenter helps in understanding the properties of triangles, especially in relation to altitudes and angles.

Front

If DL = 24 and DG is a median, what is the length of DG?

Back

DG = 8.