CK12 - Geometry

Differentstudentscan start with differenttriangles.Theycan drawdifferentlinesparallelto. But in

eachcasethe two ratios, and , are approximatelythe same.This is anotherway to say that the
two sidesof the triangleare dividedproportionally. We can provethis resultas a theorem.

TriangleProportionalityTheorem:If a line parallelto one side of a triangleintersects

the othertwo sides,then it dividesthosesidesinto proportionalsegments.

Proof.

• Given: with


• 
  

Prove:

Statement Reason

1. 
   
   
   
   1. Given
   
   
   2. Correspondinganglesare con-
      gruent
   
   
   
   

2. ,

3. AA SimilarityPostulate


4. 
   


5. , 4. Segmentadditionpostulate


6. Correspondingside lengthsin
   similartrianglesare proportional


7. 
   


8. Substitution

6.

7. Algebra


8. 
   


9. Substitution


10.