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 triangle circumcenter 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