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 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 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.

Front

How does the centroid divide each median?

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 GF is 4 and G is the centroid, what is the length of GC?

Back

8 (GC is twice the length of GF).

Front

What is the relationship between medians and centroids?

Back

The centroid is located 2/3 of the distance from each vertex along the median.

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 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.

Front

In triangle ABC, if AM is a median, what can be said about segment BC?

Back

Segment BC is divided into two equal lengths by median AM.

Front

What type of lines are altitudes in a triangle?

Back

Altitudes are always perpendicular to the side they intersect.