CK12 - Geometry

9. 
   

   True. See the solutionto problem10 to verifythis fact.

   
   


10. 
    

a. Constructthe perpendicularbisectorof. Notethat the slopeof is.

b. Point will be locatedon the perpendicularbisector. The perpendicularbisectorwill haveslope
.

c. The perpendicularbisectorwill passthroughthe midpoint and haveslope Its equation

is

d. So, the distancefrom to is equalto , whichis.

e. Considerthe distancefrom point to. Solvethe followingdistanceequationto find the coor-

dinateof point.

f. Since lies on the line , use the valueof foundfromthe equationto find the
-coordinate.

11. Showthat use CPCTCand the definitionsof bisectorand propertiesabout
    congruentadjacentanglesforminga straightangle.

AngleBisectorsin Triangles

LearningObjectives

• Constructthe bisectorof an angle.


• Applythe AngleBisectorTheoremto identifythe pointof concurrencyof the perpendicularbisectorsof
  the sides(the incenter).


• Use the AngleBisectorTheoremto solveproblemsinvolvingthe incenterof triangles.

Introduction

In our last lessonwe examinedperpendicularbisectorsof the sidesof triangles.We foundthat we were
able to use perpendicularbisectorsto circumscribetriangles.In this lessonwe will learnhow to inscribe
circlesin triangles.In orderto do this, we needto considerthe anglebisectorsof the triangle.The bisector
of an angleis the ray that dividesthe angleinto two congruentangles.

Hereis an exampleof an anglebisectorin an equilateraltriangle.