6.4 Incenter, Circumcenter, Centroid and Orthocenter

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

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 equidistant from all three vertices of the triangle.

Front

What is the Centroid of a triangle?

Back

The Centroid is the point where the three medians of a triangle intersect. It divides each median into a ratio of 2:1.

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

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 are altitudes in a triangle?

Back

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

Front

What are angle bisectors in a triangle?

Back

Angle bisectors are segments that divide an angle into two equal parts.

Front

What are perpendicular bisectors in a triangle?

Back

Perpendicular bisectors are segments that are perpendicular to a side of the triangle and bisect that side.

Front

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

Back

GC = 8 (The centroid divides each median in a 2:1 ratio).

Front

What is the relationship between the Incenter and the sides of a triangle?

Back

The Incenter is equidistant from all three sides of the triangle.