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Chapter 5 Perpendicular Bisectors. Perpendicular bisector. A segment, ray or line that is perpendicular to a segment at its midpoint. Perpendicular bisector theorem. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. . C. P. A.
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Perpendicular bisector • A segment, rayor line that is perpendicular to a segment at its midpoint
Perpendicular bisector theorem • If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
C P A B Creates an isosceles triangle!
Examples Non-Examples
Concurrent lines • When three or more lines (rays or segments) intersect in the same point Point of concurrency • The point of the intersection of the lines
Circumcenter • Point of concurrency of the perpendicular bisectors of the triangle.
Circumcenter: • Is inside an acute triangle Circumcenter!
Is on a right triangle Circumcenter!
Is outside an obtuse triangle Circumcenter!
Acute - Inside Right - On Obtuse - Outside
Perpendicular bisector formula • Circumcenter to vertices is equal distance.
B P A C
Why is this the case?? • We can circumscribe the triangle by drawing a circle with the vertices of the triangle as points on the circle. • The center of the circle is the circumcenter of the triangle for the perpendicular bisectors. • The circumcenter to the vertices are the radii of the circle.