Triangle Centers Vocabulary

Median

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

Altitude

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

Perpendicular Bisector

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

Angle Bisector

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

Circumcenter

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

Circumcenter special properties

It Is the same distance to each vertex.

Orthocenter

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

orthocenter special properties

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

Incenter special properties

Is the same distance to the sides of a triangle.

Incenter

Formed by angle bisectors of a triangle.

Centroid

The point of concurrency of the medians of a triangle.

Centroid special properties

Also known as the center of gravity.

Divides the segment into 1/3, 2/3 portions.

Centroid special properties

Where can the Incenter and Centroid be located in relation to the triangle?

These centers are always inside the triangle.

Where can the Circumcenter and Orthocenter be located in relation to the triangle?

Can be inside, outside or on the triangle.

point of concurrency

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

Equidistant

Same distance.

Midsegment

segment that connects the midpoints of two sides of a triangle

Perpendicular Bisector Theorem

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

Converse of the Perpendicular Bisector Theorem

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

Angle Bisector Theorem

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

Converse of the Angle Bisector Theorem

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