6.4 Incenter, Circumcenter, Centroid and Orthocenter

Front

What is the point of concurrency of the three medians of a triangle called?

Back

Centroid

Front

What is the point of concurrency of the three perpendicular bisectors of a triangle called?

Back

Circumcenter

Front

What is the point of concurrency of the three angle bisectors of a triangle called?

Back

Incenter

Front

What is the point of concurrency of the three altitudes of a triangle called?

Back

Orthocenter

Front

Define a median in the context of a triangle.

Back

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

Front

Define a perpendicular bisector in the context of a triangle.

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

What is an angle bisector in a triangle?

Back

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

Front

If G is the centroid of triangle ABC and GF = 4, what is the length of GC?

Back

8

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 of the opposite side.

Front

What is the significance of the circumcenter in a triangle?

Back

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