Ratios Proportions and Similarity Ratio A ratio is

Ratios, Proportions and Similarity

Ratio • • • A ratio is a comparison of 2 values by division. The ratio of 2 quantities can be written in 3 ways: a to b a: b a b (where b is not 0)

Proportion • • A proportion is a statement that 2 ratios are equal a b = c d a and d are the extremes and b and c are the means

Solving a Proportion • • Use cross products ( cross multiply) to solve a proportion. The cross product is the product of the means and the product of the extremes a b = c d Then ad = bc

SIMILAR • • 2 figures that have the same shape, but not necessarily the same size, are similar. All congruent figures are also similar

Similar polygons • In similar polygons, the corresponding angles are congruent and the corresponding sides are proportional • A similarity ratio is the ratio of 2 corresponding linear measurements in a pair of similar figures

BC= 9 = 3 and DC =12 = 3 FG 6 2 HG x 2 • 3/2 is the similarity ratio

Similarity statement • • A similarity statement is a statement indicating that 2 polygons are similar by listing their vertices in order of correspondence. Just like in congruence statements, corresponding angles have to be named in the same order.

HINT • When setting up proportions, all your ratio's numerators should come from the same figure, and all the denominators should all come from the other figure

Are all right triangles similar? • • • No, only if their acute angles have the same measure!