1. Perpendiculars and Bisectors
Chapter 5 Section 5.1
Perpendiculars and Bisectors

2. 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

3. 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

4. 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

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

8. 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

9. 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

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

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