5 3 Use Angle Bisectors of Triangles Remember

5. 3 – Use Angle Bisectors of Triangles Remember that an angle bisector is a ray that divides an angle into two congruent adjacent angles. Remember also that the distance from a point to a line is the length of the perpendicular segment from the point to the line.

5. 3 – Use Angle Bisectors of Triangles In the diagram, Ray PS is the bisector of <QPR and the distance from S to Ray PQ is SQ, where Segment SQ is perpendicular to Ray PQ.

5. 3 – Use Angle Bisectors of Triangles

5. 3 – Use Angle Bisectors of Triangles Example 1: Find the measure of <GFJ.

5. 3 – Use Angle Bisectors of Triangles Example 2: Three spotlights from two congruent angles. Is the actor closer to the spotlighted area on the right or on the left?

5. 3 – Use Angle Bisectors of Triangles Example 3: For what value of x does P lie on the bisector of <A?

5. 3 – Use Angle Bisectors of Triangles Example 4: Find the value of x.

5. 3 – Use Angle Bisectors of Triangles

5. 3 – Use Angle Bisectors of Triangles The point of concurrency of the three angle bisectors of a triangle is called the incenter of the triangle. The incenter always lies inside the triangle.

5. 3 – Use Angle Bisectors of Triangles Example 5: In the diagram, N is the incenter of Triangle ABC. Find ND.

5. 3 – Use Angle Bisectors of Triangles Example 6: In the diagram, G is the incenter of Triangle RST. Find GW.