Scale Factor

 

Scale Factor/Similarities:

Two figures are similar if:

  • They have the same shape. What does this mean?

    • It means that the corresponding angles are equal.

  • Corresponding sides change by the same scale factor. What does this mean?

    • It means that all the sides of the small figure are multiplied by the same number to obtain the lengths of the corresponding sides of the large figure.

This is two rectangles.

 

    • The scale factor of figure A to B is: 3 (3 * 3 = 9; 5 * 3 = 15)
    • The scale factor of figure B to A is: 1/3 (9 * 1/3 = 3; 15 * 1/3 = 5)
    •  

  • How does the scale factor going from the large figure to the small figure compare to the scale factor of the small figure to the large figure?

    • It is the reciprocal of the scale factor from the small to the large.

  • What is a reciprocal?

    • It is the number you multiply the first number by to get a product of 1.

    • Example: Scale factor from A to B is 3. Scale factor from B to A is 1/3

    • 3 x 1/3 = 1

  • The perimeter of the small to the large also grows by the same scale factor.

  • If the scale factor from the small to the large is s, then the area of the large figure is squared or to the second power times the area of the small figure.

Example: 3 to the second power or squared = 9 therefore:

Perimeter of A = 16

Area of A = 3 x 5 = 15

Perimeter of B = 48

16 x 3 = 48

Area of B = 135

9 x 15 = 135 (15 x 9 = 135)

  • If the ratio of corresponding sides of the two figures are equal, then the figures are similar

    • A = 3/5 = Length/Width

    • B = 9/15 = 3/5 = Length/Width

 

 

 

Worksheet

Directions: Using the diagrams below answer questions 1 and 2.

These are two triangles.

 

1. What is the scale factor from triangle CAT to triangle DOG?

 

 

2. How many times bigger is the area of triangle CAT than the area of triangle DOG?

 

3. John wanted to change Mug (x,y) into a group of evil drawings.

A) How would John change (x,y) to make Mug taller and more thin?

B) How would John change (x,y) to make Mug short and fat?

C) How would John change (x,y) to make Mug tall and fat?

4. For the shapes in A, B, and C find the missing measure.

A)

This is two rectangles.

 

X =

 

B)

 

 

This is two triangles.

 

X =

 

C)

This is two rectangles.

 

X =