3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the congruent segments. Draw a picture.

3.6—Bisectors of a Triangle Objective: Use properties of _____________ bisectors and ___________ bisectors of a __________. perpendicular angletriangle Concurrent lines: three or more lines that intersect in the _______ ________ Point of concurrency: the _________ of ________________ of concurrent lines same point point intersection

The circumcenter can be: inside the triangle (acute triangles), on the triangle (right triangles), or outside the triangle (obtuse triangles). _______________ Bisector of a triangle: a ________ that is perpendicular to a side of the triangle at the __________ of the side. ________________ of a triangle: the point of ____________________ of the perpendicular _______________ of a triangle. Perpendicular line midpoint Circumcenter concurrency bisectors

________ _____________ of a triangle: a bisector of an _________ of a triangle _______________ of a triangle: the point of __________________ of the angle bisectors Angle Bisector angle Incenter concurrency The incenter is always inside the triangle.

Construction – Perpendicular to a line from a point not on the line.

Construct a perpendicular to the given line and through the given point.

B..

Construct the Circumcenter and the Circumscribed Circle for the triangle.

Construct the Incenter and the Inscribed Circle for the triangle.