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PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School

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?.

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PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School

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  1. Scale Factors PowerPoint Presentation By Mr. Michael Braverman Haverford Middle School School District of Haverford Township Havertown, PA 1903

  2. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. a a a a

  3. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. b b b b a a a a

  4. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. b c c b c c b b a a a a

  5. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. b c c b c c b b Bottom row: a x 3 = 3a a a a a

  6. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. b c c b c c b b Right side: b x 3 = 3b a a a a

  7. Scale Factors What does it mean to have a scale factor of 3? It means that every side of the original triangle is multiplied by 3 and that all corresponding angles are congruent. b c c b c c b b Left side: c x 3 = 3c a a a a

  8. Scale Factors What does it mean to have a scale factor of 3? b c c b Perimeter of the original = a + b + c c c b b a a a a Perimeter of the copy = 3a + 3b + 3c

  9. Perimeter of the original = a + b + c Perimeter of the copy = 3a + 3b + 3c Note: Scale factor = 3 and 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.

  10. Scale Factors What does it mean to have a scale factor of 3? b c h c b 3h h c c b b h h a a a a Area of Triangle = (base x height) ÷ 2

  11. Scale Factors What does it mean to have a scale factor of 3? b c h c b 3h h c c b b h h a a a a Area of Triangle = (base x height) ÷ 2 Area of Original Triangle = (a x h) ÷ 2= ah/2

  12. Scale Factors What does it mean to have a scale factor of 3? b c h c b 3h h c c b b h h a a a a Area of Triangle = (base x height) ÷ 2 Area of New Triangle = (3a x 3h) ÷ 2 = 9ah/2

  13. Scale Factors What does it mean to have a scale factor of 3? b c h c b 3h h c c b b h h a a a a Area of Original Triangle = (a x h) ÷ 2= ah/2 Area of New Triangle = (3a x 3h) ÷ 2 = 9 x ah/2

  14. Scale Factors What does it mean to have a scale factor of 3? b c h c b 3h h c c b b h h a a a a Area of Original Triangle = (a x h) ÷ 2= ah/2 Area of New Triangle = (3a x 3h) ÷ 2 = 9 x ah/2 Therefore, if the scale factor is 3, then the area increases by a factor of 3 x 3 or 9.

  15. Scale Factors What does it mean to have a scale factor of 3? Corresponding angles must be congruent.

  16. Scale Factors To 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. c e b f a d

  17. Scale Factors To 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. c b f e Scale Factor a d So, if we are going from blueto red, and the two triangles are similar, then we have: d e f Scale factor = = = abc

  18. Scale Factors To 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. c b f e Scale Factor a d …and if we are going from red to blue, and the two triangles are similar, then we have: d e f Scale factor = = = abc

  19. Scale Factor Summary If figure B is f timesfigure 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 timesthe corresponding sides of A. • The perimeterof B is f times the perimeterof A. • The areaof B is f timesf times the areaof A. (The areaincreases by f2 ) • The angles of B are congruent to the corresponding anglesof A. • The internal ratios of A and B are equal(ex: base ÷ height)

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