Centers of Triangles

Front

What is the centroid of a triangle?

Back

The centroid is the point where all three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

What are the altitudes of a triangle?

Back

Altitudes are the perpendicular segments from each vertex of the triangle to the line containing the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices.

Front

How is the circumcenter related to the circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the orthocenter of a triangle?

Back

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

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 vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect. It is the center of the incircle, which is the circle inscribed within the triangle.

Front

What is the relationship between the incenter and the incircle?

Back

The incenter is the center of the incircle, which is tangent to all three sides of the triangle.

Front

What is the difference between the circumcenter and the orthocenter?

Back

The circumcenter is the intersection of the perpendicular bisectors of the sides, while the orthocenter is the intersection of the altitudes 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.