Section 5-1 Perpendiculars and Bisectors. Perpendicular bisector A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

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Presentation transcript:

Section 5-1 Perpendiculars and Bisectors

Perpendicular bisector A segment, ray, line, or plane that is perpendicular to a segment at its midpoint

Equidistant from two points A point that is the same distance from each point.

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

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.

A B C P

Distance from a point to a line The length of the perpendicular segment from the point to the line. –D–Distance must be perpendicular! –L–Look for right angle!

P m

Equidistant from two lines When a point is the same distance from one line as it is from another line

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

A B C If then D

Converse of 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.

A B C If then D