Perpendicular and Angle Bisectors 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)