Download Chapter 8.1 Notes

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
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
Chapter 8.2 Notes
Properties of Proportions
If a = c , then a = b
b
d
c
(Rotation)
d
If a = c , then a+ b = c + d
b
d
b
d
(Add the denominator to the numerator)
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
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
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
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 ~
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)
Chapter 8.6 Notes
Triangle Proportionality Thm
If
then
Converse of the Triangle Proportionality Thm
If
then
Thm
If
then
Thm
If
then
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’