Geometry 5-1

Perpendicular and Angle Bisectors

Geometry 5-1 Bisectors

• Equidistant- equal distance from 2 or more things

• Perpendicular Bisector- a line that goes through the midpoint of another line and makes a 90° angle.

Constructing a Perpendicular Bisector

• Draw two points and the line segment between them.

• Fold your paper over so that the two endpoints match-up. Make a crease.

• Draw a line on the crease. This is the perpendicular bisector.

Perpendicular Bisector Theorem

• Draw a few points on the perpendicular bisector that you drew.

• Draw lines from each endpoint to the points on the perpendicular bisector.

• Measure the length of each segment connected to the perpendicular bisector.

• What do you notice about those lengths?

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector, then it is equidistant from the endpoints of the segment that it bisects.

• Angle Bisector- a line the bisects an angle

Constructing an Angle Bisector

• Draw an angle

• Fold your paper so the two sides of the angle match-up with each other.

• Make a crease, and draw a line on the crease. This is the angle bisector.

Angle Bisector Theorem

• Draw a couple of points on the angle bisector that you drew.

• Draw segments connecting the sides of the angle to the points on the angle bisector. Make sure that there is an 90° angle where the segments and the side of the angle meet.

• Measure each drawn segment. • What do you notice about the lengths?

Angle Bisector Theorem

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

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints:

A(-1, 6) B(-3, -4)