5.5 Medians and Altitudes

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

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect.

Front

How do you find the length of a segment created by a median?

Back

The length of the segment from the centroid to the midpoint of the side is half the length of the median.

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

What is the orthocenter of a triangle?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

What is the relationship between medians and centroids?

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.

Front

If AC = 32 in triangle ABC, what is the length of CE if G is the centroid?

Back

CE = 16.

Front

What is the point of concurrency for the altitudes of a triangle?

Back

The orthocenter.

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 perpendicular to the opposite side.