1. Chapter 8.1 Notes
Ratio – if a and b are 2 quantities that are measured in the same units, then the ratio of a to b is a/b. (i.e. a ratio is a fraction)
Proportion – is an equation that equates 2 ratios
Means a = c Extremes
b d

2. b d Properties of Proportions
If a = c , then ad = bc (Cross Product Prop.)
b d
If a = c , then b = d (Reciprocal Prop.)
b d a c

3. Chapter 8.2 Notes Properties of Proportions
If a = c , then a = b (Rotation)
b d c d
If a = c , then a+ b = c + d
b d b d
(Add the denominator to the numerator)

4. x b Example: Find the geometric mean of 4 and 9. answer: 6
Geometric Mean – of two positive numbers a and b is the positive number x such that
a = x when solved x = √a * b
x b
Example: Find the geometric mean
of 4 and 9.
answer: 6

5. Chapter 8.3 Notes
Similar Polygons – when you have 2 polygons that have all corresponding ∠’s are ≌ and all corresponding sides are in the same proportion then they are similar (~) A X B C Y Z

6. Thm – if 2 polygons are ~, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths Scale Factor – if 2 polygons are ~, then the ratio of the lengths of 2 corresponding side is called the scale factor. We usually write scale factors like this a:b

7. Chapter 8.4 Notes
Similar Triangles 1) AA (angle-angle similarity postulate) If 2 ∠’s of one triangle are ≌ to 2 ∠’s of another triangle, then the 2 ∠’s are ~

8. Chapter 8.5 Notes
Similar Triangles 1) AA (angle-angle similarity postulate) 2) SSS (side-side-side similarity postulate) 3) SAS (side-angle-side similarity postulate)

9. Chapter 8.6 Notes
Triangle Proportionality Thm If then Converse of the Triangle Proportionality Thm

10. Thm If then

11. Chapter 8.7 Notes Dilations
1) reduction – which means it is getting smaller
A A’
2) enlargement – which means it is getting larger
A A’