powerpoint presentation by mr. michael braverman haverford middle school
DESCRIPTION
Scale Factors. PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School School District of Haverford Township Havertown, PA 1903. Scale Factors. What does it mean to have a scale factor of 3?. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/1.jpg)
PowerPoint PresentationBy
Mr. Michael BravermanHaverford Middle School
School District of Haverford TownshipHavertown, PA 1903
Scale Factors
![Page 2: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/2.jpg)
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
![Page 3: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/3.jpg)
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
![Page 4: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/4.jpg)
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
![Page 5: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/5.jpg)
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
![Page 6: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/6.jpg)
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
![Page 7: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/7.jpg)
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
![Page 8: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/8.jpg)
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
![Page 9: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/9.jpg)
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.
![Page 10: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/10.jpg)
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
![Page 11: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/11.jpg)
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
![Page 12: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/12.jpg)
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
![Page 13: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/13.jpg)
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
![Page 14: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/14.jpg)
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.
![Page 15: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/15.jpg)
Scale FactorsWhat does it mean to have a scale factor of 3?
Corresponding angles must be congruent.
![Page 16: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/16.jpg)
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
![Page 17: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/17.jpg)
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
![Page 18: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/18.jpg)
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
![Page 19: PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School](https://reader036.vdocuments.mx/reader036/viewer/2022083006/56813add550346895da327c0/html5/thumbnails/19.jpg)
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