CK-12 Geometry-Concepts

http://www.ck12.org Chapter 5. Relationships with Triangles

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/1300

James Sousa: Proof of the Perpendicular Bisector Theorem Converse

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/1301

James Sousa: Determining Values Using Perpendicular Bisectors

Guidance

Recall that aperpendicular bisectorintersects a line segment at its midpoint and is perpendicular. Let’s analyze

this figure.

←→

CDis the perpendicular bisector ofAB. If we were to draw inACandCB, we would find that they are equal.
Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint.
Perpendicular Bisector Theorem:If a point is on the perpendicular bisector of a segment, then it is equidistant
from the endpoints of the segment.
In addition to the Perpendicular Bisector Theorem, we also know that its converse is true.
Perpendicular Bisector Theorem Converse:If a point is equidistant from the endpoints of a segment, then the
point is on the perpendicular bisector of the segment.
Proof of the Perpendicular Bisector Theorem Converse:

Given:AC∼=CB

Prove:

←→

CDis the perpendicular bisector ofAB