Properties of Triangle Centers

Front

What is the definition of a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a 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 angle bisectors of a triangle intersect, and it is equidistant from all three sides.

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, and it is the center of the circumcircle.

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 the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection is the circumcenter.

Front

What is the relationship between the incenter and the triangle's sides?

Back

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

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

What are the special segments that intersect at the orthocenter?

Back

The orthocenter is formed by the intersection of the altitudes of a triangle.

Front

What is the difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is a perpendicular segment from a vertex to the line containing the opposite side.