Altitudes, Medians, & Centers

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

How do you find the length of a median in a triangle?

Back

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

What is the relationship between the centroid and the lengths of the segments created by 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 orthocenter of a triangle?

Back

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

Front

What are altitudes in a triangle?

Back

Altitudes are perpendicular segments from a vertex to the line containing the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is the center of the incircle.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle, where it would balance perfectly if made of a uniform material.

Front

If the lengths of the segments from the centroid to the vertices are 6, what are the lengths of the segments from the centroid to the midpoints of the sides?

Back

The lengths of the segments from the centroid to the midpoints of the sides would be 3, as the centroid divides each median in a 2:1 ratio.