Two figures are similar with a scale factor of 5/2. a. What is the ratio of corresponding lengths?
b. What is the ratio of their perimeters?
c. What is the ratio of their areas?
d. What is the ratio of their volumes?
e. What is the ratio of corresponding angle measures?

If we have two figures, F and F'

Such that if we start with F, and dilate it with a scale factor K, we get F'.

We will have:

All the measures of F', are K times the correspondent measures of F.

Then if F has  s₁, s₂, ..., sₙ sides, the sides of F' will be:

K*s₁, K*s₂, ..., K*sₙ

The ratio between correspondent sides will be equal to K

The ratio between perimeters will also be equal to K (because the perimeter is the sum of all the sides of each figure, so we can just take K as a common factor)

In the case of the area, because we usually multiply a measure by another, a factor K^2 will  appear, and the quotient between the areas is K^2

And finally, for the volumes, the ratio will be K^3

a) The ratio of corresponding lengths is K, in this case is 5/2

b) The ratio of the perimeters is K, in this case is 5/2

c) The ratio of the areas is K^2, in this case is (5/2)^2 = 25/4

d) The ratio of the areas is K^3, in this case is (5/2)^3 = 125/8

e) Two figures are similar if the figures have the same shape, then the corresponding angles are exactly the same, then the ratio of corresponding angle measures is 1.

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