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 TrianglesExample 1:

Find the measure of <GFJ.

5.3 – Use Angle Bisectors of TrianglesExample 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 TrianglesExample 3:

For what value of x does P lie on the bisector of <A?

5.3 – Use Angle Bisectors of TrianglesExample 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 TrianglesExample 5:

In the diagram, N is the incenter of Triangle ABC. Find ND.

5.3 – Use Angle Bisectors of TrianglesExample 6:

In the diagram, G is the incenter of

Triangle RST. Find GW.