Chapter 5 Section 5.2 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

Perpendicular Bisector Theorem Theorem Theorem 5.2 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. CA = CB is the perpendicular bisector of

Converse of the Perpendicular Bisector Theorem Theorem Theorem 5.3 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

No, would need to know that there is a right angle

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

Yes, it is possible to show that CA = CB

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. QR = SR R is on the 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

No, need to know that P is equidistant to the rays (sides of the angle)

No, distance is measured perpendicularly

1. C is on the  Bisector of 1. Given 2. Definition Bisector 3.  Bisector Theorem 4. Reflexive 5.  ADC   BDC 5. S.S.S.

1.  WOZ   WOY 1. Given 2. Def.   ’s 3. Vertical Angle Thm 4. Transitive 5. Reflexive 6.  XOZ   XOY 6. S.A.S. 7. Def.   ’s