7. Similarity.......................................................................................................................................
Ratiosand Proportions
LearningObjectives
- Write and simplifyratios.
- Formulateproportions.
- Use ratiosand proportionsin problemsolving.
Introduction
Words can havedifferentmeanings,or evenshadesof meanings.Oftenthe exactmeaningdependson the
contextin whicha wordis used.In this chapteryou’lluse the wordsimilar.
Whatdoessimilarmeaninordinarylanguage?Is a rose similarto a tulip?They’recertainlyboth flowers.Is
an elephantsimilarto a donkey?They’reboth mammals(andsymbolsof nationalpoliticalpartiesin the
UnitedStates!).Maybeyou’drathersay that a sofa is similarto a chair?In looseterms,by similarwe usually
meanthat thingsare like eachotherin someway or ways,but maybenot the same.
Similarhas a very precisemeaningin geometry, as we’ll see in upcominglessons.To understandsimilar
we first needto reviewsomebasicskillsin ratiosand proportions.
UsingRatios
Aratiois a type offraction. Usuallya ratio is a fractionthatcomparestwo parts.“The ratio of to ” can
be writtenin severalways.
•
- to
Example 1
Lookat the data below, givingsalesat BagelBonanzaone day.BagelBonanzaMondaySales
Type of bagel Numbersold
Plain
Cinnamon
Raisin
Sesame
Garlic
Wholegrain