Chapter 5 Section 2 Perpendicular and Angle

Bisectors

Objectives Students will be able to:

• Use properties of perpendicular bisectors and angle bisectors

• Apply the theorems of perpendicular and angle bisectors

Essential Understanding There is a special relationship

between the points on the perpendicular bisector of a segment and the endpoints of the segment.

There is a special relationship between the points on a bisector of an angle and the sides of the angle.

Perpendicular Bisector What do you know about perpendicular

bisectors? A right angle is formed and it splits a

segment into two equal parts Equidistant: a point that is the same

distance from two objects Which points are equidistant in the picture

below?

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

Using the Perpendicular Bisector Theorem

What is the length of QR? How would you set up the problem?

Distance from a point to a line:• The length of the perpendicular segment

from the point to the line• Length of the shortest segment• The shortest distance between two points is

a straight line

Angle Bisector Theorem If a point is on the bisector of an

angle, then the point is equidistant from the sides of the angle

Converse of the Angle Bisector Thoerem

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

What is the length of FB?

Homework Pg. 296 6-12 all, 16-22 all, 29-31 17 problems