5 2 Bisectors in Triangles Objectives Apply properties

5 -2 Bisectors in Triangles Objectives Apply properties of perpendicular bisectors and angle bisectors of a triangle. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles The circumcenter can be inside the triangle, outside the triangle, or on the triangle. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles _____ - A circle that contains all the vertices of a polygon The circumcenter of ΔABC is the center of its circumscribed circle. Holt Mc. Dougal Geometry _____ - A circle in a polygon that intersects each line that contains a side of the polygon at exactly one point. The incenter is the center of the triangle’s inscribed circle.

5 -2 Bisectors in Triangles Check It Out! Example 1 a Use the diagram. Find GM. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Check It Out! Example 1 b Use the diagram. Find GK. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Check It Out! Example 1 c Use the diagram. Find JZ. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Remember! The distance between a point and a line is the length of the perpendicular segment from the point to the line. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Unlike the circumcenter, the incenter is always inside the triangle. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Example 3 A: Using Properties of Angle Bisectors MP and LP are angle bisectors of ∆LMN. Find the distance from P to MN. Holt Mc. Dougal Geometry

5 -2 Bisectors in Triangles Example 3 B: Using Properties of Angle Bisectors MP and LP are angle bisectors of ∆LMN. Find m PMN. Holt Mc. Dougal Geometry