Bisectors in Triangles
Bisectors in Triangles
G.CO.10 Prove theorems about triangles...
Goals for this section:
Goals for this section:
To understand what a circumcenter is for a triangle.
Concurrency of Perpendicular Bisectors Theorem
Concurrency of Perpendicular Bisectors Theorem
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.
The theorem broken down:
The theorem broken down:
- "The perpendicular bisectors of the sides of a triangle..."
- So the black dotted lines in the figure are the perpendicular bisectors. They create a 90 degree angle with the sides and split the sides into two equal halves.
- "...are concurrent at a point..."
- This means that we're looking at the point where the dotted lines intersect.
- "...equidistant from the vertices."
- That point we're looking at is the same distance away from all the vertices. Vertices are the "corners" of the triangle.
Circumcenter
Circumcenter
This is the "center" of the triangle, where those dotted lines meet. The circumcenter is equidistant to all the vertices.
Source: Pearson Integrated High School Mathematics Textbook
Circumcenter of a Triangle
Circumcenter of a Triangle
External Resources
External Resources
Keywords: concurrency of perpendicular bisectors theorem, circumcenter, triangle, acute, right, obtuse