Circumcenter, Incenter, centroid, orthocenter

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 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 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

Define 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.

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

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 an angle bisector?

Back

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

Front

If CF, BE, and AD are the medians of triangle ABC and BF = 10, what is AF?

Back

AF = 10 (The centroid divides the median into a 2:1 ratio).

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle and is parallel to the third side.