Ratios,%20Proportions%20and%20Similarity

1
Ratios,Proportions and Similarity
2
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)

3
Proportion

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

4
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

Then ad bc
a c b d
5
SIMILAR

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

6
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

7
BC 9 3 and DC 12 3FG 6 2
HG x 2

• 3/2 is the similarity ratio

8
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.

9
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

10
Are all right triangles similar?

• No, only if their acute
• angles have the
• same measure!

11
(No Transcript)