2.8 Proportions and Similar Figures

2.8 Proportions and Similar Figures Proportion: is an equation that states that two ratios are equal. Similar Figures: two figures that have the same shape but not necessarily the same size. Scale Drawing: is a drawing that is similar to an actual object or place. Scale: The ratio of any length of a drawing to the actual length of the object. Scale Model: is a three dimensional model that is similar to a three dimensional object.

Real World:

Proportion: For a, b, c , d and b≠0 and d≠0,If Then =

In order for us to solve the boat problem, we must understand similarity ( ): We can find proportions to find missing sides of similar ( ) figures. x Since the two figuresare similar. We can set a proportion to solve for the missing length: = We must math sides, that is big under big and small under small.

x = 16(3)=8(x) 48=8(x) __ ___ 8 8 6 = X Thus, the length of the big width is 6 units.

YOU TRY IT: Provide the measure of the missing variables if the figures are similar. 30 CM Z X 4CM 24 CM Y 3 CM 9 CM

YOU TRY IT (Solution): Using Proportions we set the following: 30 CM = 3X = 9(4) X= 12 cm Z X 4CM Y 24 CM = 3 CM 9 CM 9Y = 3(24) Y= 8 cm = 9Z = 3(30) Z= 10 cm The measure of the missing variables are :x = 12cm, y = 8 cm, and z = 10 cm.

YOU TRY IT: Now let’s solve the boat problem:

BOAT PROBLEM (Solution): = Set up proportion x(12) = 9(4) Cross Product 12x= 36 Inverse of multiplication ___ ____12 12 Don’t forget to check! x = 3

YOU TRY IT: An 8-oz can of orange juice contains about 97 mg of vitamin C. About how many milligrams of vitamin C are there in a 12-oz can of orange juice?

YOU TRY IT (Solution): = Set up proportion x(8oz) = 97mg(12oz) Cross Product 8oz(x) =1164mgoz Multiplication Inverse of multiplication 8oz(x) =1164mgoz ________ _________ 8oz 8oz X = 145.5 mg Don’t forget to check!

Class Work: Pages: 127-128 Problems: 11, 17, 19, 25, 34, 35, 36, 40, 48, 49, 50, 51

2.8 Proportions and Similar Figures