CK12 - Geometry

4. 
   

   Thereis no need.With the and partsof we havetriangleswith two congruentangles.The
   trianglesare similarby AA.

   
   


5. 
   

   Yes

   
   


6. 
   

   No

   
   


7. 
   

   No

   
   


8. 
   

   Yes

   
   


9. 
   

   No

   
   


10. 
    

    Yes

    
    


11. 
    

A. Yes

B. Yes

C. Yes. All threepairsof anglesare congruent,so the trianglesare similarby AAA or AA.

ProportionalityRelationships

LearningObjectives

• Identifyproportionalsegmentswhentwo sidesof a triangleare cut by a segmentparallelto the third
  side.


• Dividea segmentinto any givennumberof congruentparts.

Introduction

We’ll wind up our studyof similartrianglesin this section.We will also extendsomebasicfactsaboutsimilar
trianglesto dividingsegments.

DividingSidesof TrianglesProportionally

Thinkabouta midsegmentof a triangle.A midsegmentis parallelto one side of a triangle,and that it divides
the othertwo sidesinto congruenthalves(becausethe midsegmentconnectsthemidpointsof thosetwo
sides).So the midsegmentdividesthosetwo sidesproportionally.

Example 1

Explainthe meaningof "the midsegmentdividesthe sidesof a triangleproportionally."

Supposeeachhalf of one side of a triangleis unitslong,and eachhalf of the otherside is unitslong.