CK12 - Geometry

4. DistributiveProperty


5. 
   


6. Substitution


7. 
   


8. Substitution


9. 
   


10. CrossMultiplicationTheorem


11. 
    

This secondtheoremis nearlythe sameas the previous,

Corollary5:If , , , and , and , then

The proofof this corollaryis in the LessonExercises.

Example 2

Supposewe’regiventhat again,as in example1.

Hereare someotherproportionsthat mustalso be true, and the theoremsthat guaranteethem.

Corollary 4

Corollary 5

Corollary 4

LessonSummary

Proportionswereprobablynot new to you in this lesson;you may havestudiedthemin previouscourses.
Whatprobablyis new is the largerstructureof theoremsand corollariesthat serveas toolsfor workingwith
proportions.

The mostbasicfact aboutproportionsis the CrossMultiplicationTheorem:

assuming. The corollariesin this lessonare reallyjust variationson the CrossMulti-
plicationTheorem.Theymay be usefulin problems,but we couldalwaysrevertbackto CrossMultiplication
if we had to.

Somepeoplefind proportionsnice to workwith,becausethereare so manydifferent—andcorrect—ways
to writea givenproportion,as you saw in the corollaries.It sometimesseemsthat you wouldreallyhaveto