Perpendicular Bisectors of Triangles
The perpendicular bisector for each segment is given. Arrange the segments to make different triangles.
Perpendicular Bisectors of Triangles
What do you notices as you arrange the segments?
Circumcenter
If three or more lines intersect at a single point, then the lines are concurrent lines The point where three or more lines intersect is called a point of concurrency. The point of concurrency for perpendicular bisectors is called the circumcenter.
The perpendicular bisector for each side of triangle ABC is given. Move the vertices to make different triangles.
Perpendicular Bisectors of Triangles
What do you notice about the circumcenter D? Use the distance measuring feature to find the distance from the point D to each vertex. Manipulate the triangle one more time. What do you notice?
Circumcenter Theorem
The circumcenter of any triangle is equidistant to the vertices of the triangle.