Post on 05-Jan-2016
description
PowerPoint PresentationBy
Mr. Michael BravermanHaverford Middle School
School District of Haverford TownshipHavertown, PA 1903
Scale Factors
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa a
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
Bottom row: a x 3 = 3a
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
Right side: b x 3 = 3b
It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
Left side: c x 3 = 3c
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
Perimeter of the original = a + b + c
Perimeter of the copy = 3a + 3b + 3c
Perimeter of the original = a + b + cPerimeter of the copy = 3a + 3b + 3cNote:
Scale factor = 3and
3 (a + b + c ) = 3a + 3b + 3c(This IS the distributive property!)
Therefore, the perimeter of the copy = the scale factor times the perimeter of the original.
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
h hh
h3h
Area of Triangle = (base x height) ÷ 2
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
h hh
h3h
Area of Triangle = (base x height) ÷ 2Area of Original Triangle = (a x h) ÷ 2= ah/2
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
h hh
h3h
Area of Triangle = (base x height) ÷ 2Area of New Triangle = (3a x 3h) ÷ 2 = 9ah/2
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
h hh
h3h
Area of New Triangle = (3a x 3h) ÷ 2 = 9 x ah/2
Area of Original Triangle = (a x h) ÷ 2= ah/2
Scale FactorsWhat does it mean to have a scale factor of 3?
a aa ab b
bb
c cc
c
h hh
h3h
Area of New Triangle = (3a x 3h) ÷ 2 = 9 x ah/2
Area of Original Triangle = (a x h) ÷ 2= ah/2
Therefore, if the scale factor is 3, then the area increases by a factor of 3 x 3 or 9.
Scale FactorsWhat does it mean to have a scale factor of 3?
Corresponding angles must be congruent.
Scale FactorsTo find a scale factor between objects, take the side of the figure
you are going TO and write it as the numerator. Take the
corresponding side of the figure you are coming FROM and
write it as the denominator.
a
bc
d
ef
Scale FactorsTo find a scale factor between objects, take the side of the figure you are going TO and
write it as the numerator. Take the corresponding side of the figure you are coming
FROM and write it as the denominator.
a
bc
d
ef
So, if we are going from blue to red, and the two triangles are similar, then we have:
Scale factor = = = d e f a b c
Scale Factor
Scale FactorsTo find a scale factor between objects, take the side of the figure you are going TO and
write it as the numerator. Take the corresponding side of the figure you are coming
FROM and write it as the denominator.
a
bc
d
ef
…and if we are going from red to blue, and the two triangles are similar, then we have:
Scale factor = = = d e f a b c
Scale Factor
If figure B is f times figure A then:• f is the scale factor from A to B.• The scale factor from B to A = 1/f • The lengths of the sides of B are f times the corresponding
sides of A.• The perimeter of B is f times the perimeter of A.• The area of B is f times f times the area of A. (The area
increases by f 2 )• The angles of B are congruent to the corresponding angles
of A.• The internal ratios of A and B are equal (ex: base ÷ height)
Scale Factor Summary