Medians and Altitudes of Triangles

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 line 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

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 90-degree angle.

Front

How do you find the length of a segment when given a median?

Back

The median divides the opposite side into two equal segments, so if one segment is known, the other is equal.

Front

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

Back

CE = 16, because the centroid divides each median into a 2:1 ratio.

Front

What is the relationship between the centroid and the medians of a triangle?

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

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal angles.

Front

If CF, BE, and AD are the medians of a triangle, and BF = 10, what is AF?

Back

AF = 10, because the median divides the opposite side into two equal segments.