http://www.ck12.org Chapter 5. Relationships with Triangles
Perpendicular Bisectors and Triangles
Two lines intersect at a point. If more than two lines intersect at the same point, it is called a point of concurrency.
Point of Concurrency:When three or more lines intersect at the same point.
Investigation 5-1: Constructing the Perpendicular Bisectors of the Sides of a Triangle
Tools Needed: paper, pencil, compass, ruler
- Draw a scalene triangle.
- Construct the perpendicular bisector (Investigation 1-3) for all three sides.
The three perpendicular bisectors all intersect at the same point, called the circumcenter.
Circumcenter:The point of concurrency for the perpendicular bisectors of the sides of a triangle.
- Erase the arc marks to leave only the perpendicular bisectors. Put the pointer of your compass on the circumcenter.
Open the compass so that the pencil is on one of the vertices. Draw a circle. What happens?
The circumcenter is the center of a circle that passes through all the vertices of the triangle. We say that this circle
circumscribesthe triangle. This means thatthe circumcenter is equidistant to the vertices.