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

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

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

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

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

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

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.

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

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

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

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

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

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. a b c d e f

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. a b c d e f 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 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. a b c d e f …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