Triangle Centers Vocabulary

a segment joining the vertex to the midpoint of the opposite side.

A perpendicular segment from a vertex to the line containing the opposite side. the height.

A line that is perpendicular to a segment at its midpoint.

a line, segment, or ray that divides an angle into two congruent angles

Formed by the intersection of the perpendicular bisectors of a triangle.

It Is the same distance to each vertex.

The point of concurrency of the three altitudes of a triangle.

Will be in an acute ∆, on a right ∆, & outside an obtuse ∆.

Is the same distance to the sides of a triangle.

Formed by angle bisectors of a triangle.

The point of concurrency of the medians of a triangle.

Also known as the center of gravity.

Centroid special properties

These centers are always inside the triangle.

Can be inside, outside or on the triangle.

The point where three or more lines intersect. (Circumcenter, Incenter, Centroid or Orthocenter)

Same distance.

segment that connects the midpoints of two sides of a triangle

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle