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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 1 (part:part) 4 OR 1 5 (part:whole, because there are 5 parts altogether) Ratio Word Problems • • 3. Attach an X to each part of the ratio Write and solve an equation using the expressions 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. 5. The ratio of two supplementary angles is 4 : 1. Find the angles. 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 shape size Example of similar triangles • • • • congruent Their corresponding angles are _______________. direct ratio Their corresponding sides are in a ___________________. scale factor 2:1 This ratio is called a _______________ and in this case is ____. We show that they are similar with this statement: ____________.