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Geom 6.3 Angle Bisectors of Triangles Angle Bisectors of Triangles An angle bisector of a triangle is a segment that bisects an angle of the triangle. One endpoint is on the vertex of the angle, and the other endpoint is on the opposite side of the triangle. An angle bisector is a segment that _______________________. 15 14 13 12 11 10 4 Angle Bisectors of Triangles 9 8 0° Any triangle has _____ angle bisectors. 7 179 6 Let's construct one below. 5 2 4 3 2 1 0 51° 0 1 3 5 Geom 6.3 Angle Bisectors of Triangles Angle Bisectors of Triangles Draw any triangle. Then use a protractor to measure the angles and draw the three angle bisectors. Angle Bisectors of Triangles The three angle bisectors of a triangle meet in one point the incenter. Geom 6.3 Angle Bisectors of Triangles Constructions Review Geometry constructions use only a compass and a straight edge. The site www.mathopenref.com/constructions.html has several nice animations for lots of different constructions. Use these animations to construct the following Triangle Centers: 1. Centroid (Intersection of the three medians of a triangle). 2. Orthocenter (Intersection of the three altitudes of a triangle). 3. Incenter (Intersection of the three angle bisectors). 4. Circumcenter (Intersection of the three perpendicular bisectors). If you make your constructions into a poster that can be displayed with descriptions, you will receive extra points.