Medians of Triangles

Front

What is the centroid of a triangle?

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 a median in a triangle?

Back

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

Front

If a median divides a triangle into two smaller triangles, what can be said about their areas?

Back

The two smaller triangles have equal areas.

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 lengths of the segments created by a 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.

Front

If BE = 15 and G is the centroid, what is the length of EG?

Back

EG = 5, since the centroid divides the median in a 2:1 ratio.

Front

What is the formula to find the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median, and c is the length of 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 the difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.

Front

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

Back

AF = 10, since the centroid divides the median in a 2:1 ratio.