5.2.2 Use Perpendicular Bisectors

SWBAT:Define Concurrency. Define Circumcenter.

You will accomplish this for homework

When 3 or more lines, rays, or segments intersect in the same point, they are called concurrent lines, rays, or segments.

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

Point of concurrency

Concurrent

Not Concurrent

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle

This point of concurrency is called the Circumcenter of the triangle

AD DC DB

A

B

C

D

Obtuse trianglecircumcenter is outside of the triangle

Since the circumcenter is equidistant from the vertices of the triangle, it is the center of a circle that passes through all three vertices

The vertices of the triangle are all on radii by the definition of circles

3 rules: Acute: Circumcenter is inside the triangle Right: Circumcenter is on the triangle Obtuse: Circumcenter is outside of the

triangle

Right triangle: Acute triangle:

Obtuse triangle:

P. 306   16, 17, 20 – 22, 30 for 20 – 22

◦ To help justify your answer draw 3 triangles for each problem, some may need to be non-examples

◦ Draw the perpendicular bisectors and circles for each triangle as needed