Introduction to Geometry: Parallel and Perpendicular Lines

Properties of a Perpendicular Bisector

Analyze the following properties of perpendicular bisectors.

Property 1
The distances of any point on the perpendicular bisector from both endpoints of the line being bisected are the same.

perpendicular line segments B D and A R, that intersect at point F, segments drawn from point A to point B and from point A to point D

In the figure above, line segment A R is the perpendicular bisector of line segment B D. Thus, AB = AD.

Property 2
If any point on the perpendicular bisector is connected to the endpoints of the segment being bisected, the angles formed at the endpoints are congruent.

perpendicular line segments B D and A R, that intersect at point F, segments drawn from point A to point B and from point A to point D

In this figure, line segment A R is perpendicular bisector of line segment B D. Then angle A B F is congruent to angle A D F.