PERPENDICULAR BISECTORS SECTION 5.2. PERPENDICULAR BISECTOR THEOREM A point is on the perpendicular bisector if and only if it is equidistant from the.

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Presentation transcript:

PERPENDICULAR BISECTORS SECTION 5.2

PERPENDICULAR BISECTOR THEOREM A point is on the perpendicular bisector if and only if it is equidistant from the endpoints of the segment.

EXAMPLE 1 Use the Perpendicular Bisector Theorem AD = CD Perpendicular Bisector Theorem 3x x =5x = Substitute. 7 x = Solve for x. BD is the perpendicular bisector of AC. Find AD. AD = 5x = 5(7) = 35. ALGEBRA

CONCURRENCY The point of intersection of the lines, rays, or segments is called the point of concurrency.

POINTS OF CONCURRENCY The point of concurrency of the three perpendicular bisectors a triangle is called the circumcenter. The circumcenter can be inside, on, or outside the triangle.

WHAT IS SPECIAL ABOUT THE CIRCUMCENTER? The perpendicular bisectors of a triangle intersect at a point that is equisdistant from the vertices of the triangle. PA = PB = PC

ASSIGNMENT p. 306: 3-5,11-17