Centers of Triangles

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also known as the center of mass or balance point of the triangle.

Front

What segments intersect at the orthocenter of a triangle?

Back

The orthocenter is the intersection point of the three altitudes of a triangle.

Front

What is 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 circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of a triangle intersect.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

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

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 vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

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 point is the circumcenter.

Front

What is the significance of the orthocenter in a triangle?

Back

The orthocenter can be inside, outside, or on the triangle, depending on the type of triangle (acute, obtuse, or right).

Front

What is an angle bisector?

Back

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