Points of Concurrency Practice

Front

What is the definition of an altitude of a triangle?

Back

A line segment drawn from a vertex perpendicular to the opposite side or to the line containing the opposite side.

Front

What is the definition of a median of a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

The point where the medians of a triangle intersect.

Front

What is the orthocenter of a triangle?

Back

The point where the altitudes of the triangle intersect.

Front

What is the circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides of the triangle intersect.

Front

What is the incenter of a triangle?

Back

The point where the angle bisectors of the triangle intersect.

Front

How many points of concurrency are there in a triangle?

Back

There are four points of concurrency: centroid, orthocenter, circumcenter, and incenter.

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 longer segment being twice the length of the shorter segment.

Front

What is the significance of the orthocenter in a triangle?

Back

The orthocenter can be inside, outside, or on the triangle, depending on the type of triangle (acute, obtuse, or right).

Front

What is the relationship between the circumcenter and the circumcircle?

Back

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