Perpendiculars and Bisectors Chapter 5 Section 5.1 Perpendiculars and Bisectors

Vocabulary Perpendicular Bisector: A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector Equidistant: Being the same distance away from two or more objects A point can be equidistant from two other points A point can be equidistant from two lines Distance from a point to a line: Defined to be the length of a segment through the point perpendicular to the line

is the perpendicular bisector of Perpendicular Bisector Theorem Theorem Theorem 5.1 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. is the perpendicular bisector of CA = CB

T is on perpendicular bisector of Converse of the Perpendicular Bisector Theorem Theorem Theorem 5.2 Converse Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of a segment. CT = DT T is on perpendicular bisector of

Yes, since  CA = CB Thus C is on the perpendicular bisector

R is on the angle bisector of QPS Angle Bisector Theorem Theorem Theorem 5.3 Angle Bisector Theorem If a point is on the angle bisector of an angle, then it is equidistant from the two sides of the angle. R is on the angle bisector of QPS QR = SR

R is on angle bisector of QPS Converse of the Angle Bisector Theorem Theorem Theorem 5.4 Converse Angle Bisector Theorem If a point is equidistant from the two sides of the angle, then it is on the angle bisector of an angle. QR = SR R is on angle bisector of QPS

1. C is on the  Bisector of 1. 2. 3. 4. 5. ADC  BDC 5.

1. WOZ  WOY 1. Given 2. 3. 4. 5. 6. XOZ  XOY 6. 7.