Centers of Triangles

Front

What is the definition of an angle bisector?

Back

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

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect, and it is equidistant from all three vertices.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is the center of mass of the triangle.

Front

What is a median in a triangle?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a line segment into two equal parts at a 90-degree angle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

Front

If G is the centroid of triangle ABC and BE = 18, what is the length of BG?

Back

BG = 12 (The centroid divides each median in a 2:1 ratio).

Front

What is the relationship between the circumcenter and the circumradius?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle, centered at the circumcenter.

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.

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median, and c is the length of the opposite side.