Geometry Chapter 8 Outline
8.1 Ratios and Proportions page 418-420; 2-44 x2 due ______________
Ratio:
Proportion:
Forms of writing proportions:
Extended proportions:
Properties of Proportions:
𝑎
𝑐
=
𝑖𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜:
𝑏
𝑑
(1) 𝑎𝑑 = 𝑏𝑐
(2)
𝑏
𝑑
=
𝑎
𝑐
(3)
𝑎
𝑏
=
𝑐
𝑑
(4)
𝑎+𝑏
𝑐+𝑑
=
𝑏
𝑑
Cross-product Property
Means and extremes
Ex: If 𝐼𝑓
𝑥
𝑦
=
5
6
Scale drawing:
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8.2 Similar Polygons
page 425-427; 2-48 x2 due ___________
Two polygons are similar if _______________________________________________________ and
____________________________________________________________________
The similarity ratio is
You can determine if polygons are similar by
1) _______________________________________________________________________________ and
2) _______________________________________________________________________________
Finding unknown lengths in similar polygons:
Solve for x min these similar polygons.
6 cm
5 cm
3.2 cm
2 cm
X cm
Golden Rectangle
Golden Ratio: 1.618 : 1
2
8.3 Proving Triangles Similar page 435-437; 2-38 x2 due ________________
Postulate 8-1 AA Similarity Postulate
If ___________________ of one triangle are congruent to ___________________ of another triangle,
then the triangles are similar
̴.
Theorem 8-1 Side-Angle-Side Similarity Theorem
If
And
Then
Theorem 8-2 Side-Side-Side Similarity Theorem
If
Then
Ex
Indirect Measurement
3
8-4 Similarity in Right Triangles page 442-443; 2-36 x2, 40-48 x2 due ______________
Theorem 8-3
The ___________________ to ____________________________ of a __________________________
divides the triangle into __________________________________ that are _______________________
to ________________________________________ and ______________________________________
Geometric Mean
The geometric mean of two ___________________________________ is the positive number x such
that ________________________________________
Ex: find the geometric mean of 4 and 18.
Corollary 1 to Theorem 8-3
The length of the _____________________________________ to the ____________________________
of a ________________________________________________ is the geometric mean of the
____________________________________________________________________________________.
C
A
D
B
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Corollary 2 to Theorem 8-3
The _______________________________________________________________ of a
__________________________________________ separates the _____________________________ so
that the length of ___________________________________________ of the triangle is the
____________________________________________________ of the length of the adjacent
hypotenuse segment and the length of the _________________________________________.
Ex: find x and y
x
y
4 in
5 in
8-5 Proportions in Triangles page 448-451; 2-26 x2, 28-32 x2, 38-50 x2 due _______________
Theorem 8-4 Side-Splitter Theorem
If a line is _______________________ to one side of a triangle and _________________________ the
_____________________________________, then it _____________________ those sides
_______________________ .
Q
R
X
S
Y
If QS = 7, SY = 5 and QR = 3, find RX
5
Corollary to Theorem 8-4
If three _____________________________ intersect two ___________________________, then the
________________________ intercepted on the ___________________________ are
_______________________________
𝑎
𝑏
=
𝑐
𝑑
b
a
d
c
Theorem 8-5 Triangle-Angle-Bidsector Theorem
If a _________________ bisects the _______________________________________, then it divides the
____________________________________ into ______________________________ that are
________________________ to the ______________________________________________________.
Ex: Find the value of x
R
5
Q
8
P
6
x
S
6
8-6 perimeters and Areas of Similar Figures page 456; 2-32 x2, 35-37 due ________________
Theorem 8-6 Perimeters and Areas of Similar Figures
If the _______________________________ of two similar figures is __________________,
Then (1) the ratio of their perimeters is
And (2) the ratio of their areas is
Ex:
6m
9m
A) Find the ratio (smaller to larger)
Of the perimeters.
B) Find the ratio (smaller to larger) of the areas.
Ex: the areas of two similar triangles are 50 sq. cm and 98 sq cm.
A) What is the similarity ratio?
B) What is the ratio of their perimeters?
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