1. Obj. 20 BisectorsThe student is able to (I can): Construct perpendicular and angle bisectors Use bisectors to solve problems Identify the circumcenter and incenter of a triangle

2. Thm 5-1-1 Perpendicular Bisector TheoremIf a point is on the perpendicularbisector of a segment, then it isequidistant from the endpoints of thesegment.PDAEPD = ADPE = AE 3. Thm 5-1-2 Converse of Perp. Bisector TheoremIf a point is equidistant from theendpoints of a segment, then it is on theperpendicular bisector of the segment.SKT YST = YT 4. Examples Find each measure:1. YOYO = BO = 152. GRBOY15GIR20 202x-1 x+8L2x 1 = x + 8x = 9GR = 2x 1 + x + 8 = 34 5. Thm 5-1-3Thm 5-1-4Angle Bisector TheoremIf a point is on the bisector of an angle,then it is equidistant from the sides ofthe angle.AN AN = GNL GConverse of the Angle Bisector TheoremIf a point is equidistant from the sidesof an angle, then it is on the anglebisector.ALN @ GLN 6. circumcenter The intersection of the perpendicularbisectors of a triangle. 7. circumcenter The intersection of the perpendicularbisectors of a triangle.It is called the circumcenter, because it isthe center of a circle that cccciiiirrrrccccuuuummmmssssccccrrrriiiibbbbeeeessssthe triangle (all three vertices are on thecircle). 8. incenter The intersection of the angle bisectors of atriangle. 9. incenter The intersection of the angle bisectors of atriangle.It is called the incenter because it is thecenter of the circle that is iiiinnnnssssccccrrrriiiibbbbeeeedddd in thecircle (the circle just touches all threesides).