DO NOW ft 4ft On a Sunny Day, a person who is 6ft tall casts a 4ft shadow. This is proportional to the height of a nearby flagpole which casts a 16ft shadow. How tall is the flagpole? Height Shadow Cast 6ft4 ft X ft16 ft Answer: The flagpole casts a shadow that is 4 times larger than the person’s shadow. Therefore, the proportional flagpole has a height 4 times larger than a 6 ft person. The flagpole is 24 ft tall.

A proportional relationship is a set of equivalent ratios. Equivalent ratios have different values, but are in the same ratio. To generate 2 an equivalent ratio, multiply or divide each quantity in a ratio by the same value. What are some ways we can prove that these ratios are proportional? = = Lowest term: 2 3 Equivalent 4 6 = =

9x 112 x 10 5 x 1188 The length is 9 times larger than the height, therefore: X = (12)(9) or 108.

x x9 3 x Based on number values only, which other problem on this page is similar? (3)(110) = (10)(x) 330 = 10x = x

x The figures are in different orientations. X corresponds to _____? x x The figures are in different orientations. X corresponds to _____? 3 The figures are in different orientations. X equals _____? 7