Chapter 6 Vocabulary and Theorems

Front

Perpendicular Bisector Theorem (Thm. 6.1)

Back

In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

Converse of the Perpendicular Bisector Theorem (Thm. 6.2)

Back

In a plane, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

Front

The Angle Bisector Theorem (Thm. 6.3)

Back

If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.

Front

Converse of the Angle Bisector Theorem (Thm. 6.4)

Back

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

Front

Concurrent Lines, Rays or Segments

Back

Three or more lines, rays, or segments that intersect at one point.

Front

Perpendicular Bisector of a Triangle

Back

The point of concurrency of the 3 perpendicular bisectors of a triangle.

Front

Pt P is the circumcenter.

Back

The circumcenter P is equidistant from the three vertices, so P is the center of a circle that passes through all three vertices.

Front

Angle Bisector of a Triangle

Back

A ray that divides an angle of a triangle into two congruent adjacent angles.

Front

Incenter of a Triangle

Back

The point of concurrency of the 3 angle bisectors of a triangle.

Front

Circumcenter Theorem (Thm. 6.5)

Back

The perpendicular bisectors of the sides of a triangle are concurrent at the circumcenter, which is equidistant from the vertices of the triangle.