CK12 - Geometry

We will start by summarizingthe giveninformationand whatwe wantto prove.Thenwe will use a two-
columnproof.

Given: , , , and are real numbers,with and and

• Prove:

Statement Reason

1. , , , and are real numbers,with 1. Given
   and
   2. Given


2. 
   


3. , identitypropertyof multipli-
   cation

3.

4. Commutativepropertyof multiplication


5. 
   


6. If equalfractionshavethe samedenomi-
   nator, thenthe numeratorsmustbe equal


7. or

This theoremallowsyou to use the methodof crossmultiplicationwith proportions.

LessonSummary

Ratiosare a usefulway to comparethings.Equalratiosare proportions.Withthe Means-and-Extremes
Theoremwe havea simplebut powerfulmethodfor solvingany proportion.

Pointsto Consider

Proportionsare very “forgiving”—thereare manydifferentwaysto writeproportionsthat are equivalentto
eachother. Thereare hintsof someof thesein the LessonExercises.In the next lesson,we’ll provethat
theseproportionsare equivalent.

You knowaboutfiguresthat arecongruent. But manyfiguresthat arealikeare not congruent.Theymay
havethe sameshape,eventhoughthey are not the samesize.Thesearesimilarfigures;ratiosand pro-
portionsare integralto definingand understandingsimilarfigures.

LessonExercises

The votesfor presidentin a club electionwere:

Suarez, Milhone, Cho,

1. Write eachof the followingratiosin simplestform.

a. votesfor Milhoneto votesfor Suarez

b. votesfor Cho to votesfor Milhone

c. votesfor Suarezto votesfor Milhoneto votesfor Cho