1. Perpendicular Bisectors of a Triangle Geometry

2. Equidistant A point is equidistant from two points if its distance from each point is the same.

3. PERPENDICULAR BISECTOR THEOREM If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

4. CONVERSE OF THE PERPENDICULAR BISECTOR THEOREM If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

5. PERPENDICULAR BISECTOR OF A TRIANGLE A perpendicular bisector of a triangle is a line (ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side.

6. 3 Perpendicular Bisectors in every triangle!

7. VOCAB Concurrent lines – Three or more lines (rays or segments) that intersect at the same point. Point of Concurrency – The point of intersection of concurrent lines. Circumcenter of the triangle – The point of concurrency of the perpendicular bisectors of a triangle.

8. CONCURRENCY OF PERPENDICULAR BISECTORS OF A TRIANGLE The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.

9. Point of Concurrency Circumcenter of the Triangle The circumcenter of the triangle can be inside the triangle, on the triangle, or outside the triangle.

10. Where to meet?