chapter 5 perpendicular bisectors. perpendicular bisector a segment, ray or line that is...
TRANSCRIPT
Chapter 5Perpendicular 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.
A B
C
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Creates an isosceles triangle!
Examples Non-Examples
Perpendicular bisector of a triangle
• A line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side.
Perpendicular Bisector
Concurrent lines• When three or mores 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 triangleCircumcenter!
• Is outside an obtuse triangle
Circumcenter!
Acute - Inside
Right - On
Obtuse - Outside
Perpendicular bisector formula
• Circumcenter to vertices is equal distance.
P
B
CA
PCPBPA