Transcript 5.3 – Use Angle Bisectors of Triangles

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.