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 = c b d a and d are the extremes and
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 Then ad = bc
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 = and DC =12 = 3 FG HG x
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!