Ratios, Proportions, and Similar Triangles

Ratios

• Ratios are like fractions• The ratio 1:4 means 1 part to 4 parts

and is equivalent to the fraction

(part:part)

OR (part:whole, because there are 5 parts altogether)

1

5

1

4

Ratio Word Problems• Attach an X to each part of the ratio• Write and solve an equation using the expressions

3. The ratio of two complementary angles is 1 : 2. Find the angles.

<1 = 1x, <2 = 2x

1x + 2x = 90

3x = 90; x = 30

<1 = 30, <2 = 60

4. The ratio of two supplementary angles is 4 : 1. Find the angles.

5. The ratio of the angles of a triangle is 2 : 3 : 7. Find the angles.

A. Solving Proportions

• Cross multiply and set the products equal to each other

• Be sure to use FOIL when multiplying polynomials

• Solve for the variable

B. Properties of proportions

Similar Polygons

Example of similar triangles

• Their corresponding angles are _______________.• Their corresponding sides are in a ___________________.• This ratio is called a _______________ and in this case is ____.• We show that they are similar with this statement: ____________.

shape size

scale factor 2:1

congruent

direct ratio