5-2 Perpendicular and Angle Bisectors

Learning Goals 1. To use properties of perpendicular bisectors and angle bisectors.

Equidistant Equal distance

Perpendicular Bisector A line that passes through the midpoint of a segment and is perpendicular to that segment.

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

Perpendicular Bisector Theorem If CD is a perpendicular bisector of AB, then PA = PB. D A B C P

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.

Converse of the Perpendicular Bisector Theorem If PA = PB, then CD is a perpendicular bisector of AB. D AB C P

When a runner sees the finish line what happens? Finish Line

What direction do they run? Finish Line

They always run straight at the finish line. Finish Line

Why? Finish Line

Because it is the shortest distance. Finish Line

The runners path and the finish line make what type of angle? Finish Line

Distance between a Point and a Line The distance from a point to a line is the length of the segment perpendicular to the line from the point.

Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Angle Bisector Theorem If AD bisects CAB, then DB = DC. B D C A

Converse to the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle.

Converse to the Angle Bisector Theorem If DB = DC, then AD is a bisector of BAC. B D C A

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