Download McDougal Geometry chapter 6 notes

Mrs. Jones’s Mathography
I was born as Jenny Dai, but since my marriage to Mr. Matt Jones 196 years ago, I
became Mrs. Jones. That is also what I like to be called. I live with 3 64 others at my
home: my husband Matt, my daughters Eden and Klara, and my mother Shunu. Matt has
a Ph. D in Mathematics and is a professor at Cal State Dominguez
Hills (home of the LA

Galaxy soccer team). Eden was born on the (n1) th day where 180(n1  2)  4500 in
the [n2] th month where e n2  2981of the year (2*103)+3. Klara was born on the (n3) th
day where 180(n 3  2)  2520in the (n4)th month where log 5 n 4  1 of the year

(2*103)+8.

 Taiwanese, and English at home, and am currently trying to teach all
I speak Mandarin,
 languages to Eden and Klara. My interests, talents,

[π]
and hobbies include country line
dancing, reading, traveling, collecting college t-shirts (I have ( [15.6 ] ) in my collection),
and eating (In the last [19.1 ] months, I have eaten at [115.9 ] different restaurants,
[34.1 ]of them multiple times). I am proud of being a math teacher at Kennedy, where I
graduated in 25(80-π)+25π –7 (before all of you were born). My birthday is the [9.3 ] th

day of the [1.3 ] th month, in the year of 25(80-π)+25π -25.


I was a good math student from kindergarten through UCLA (where I received my
bachelors and masters degrees). I liked when teachers tried to make math make sense
and not just make me blindly follow procedures. I also enjoyed seeing some of the reallife applications of math. As a teacher, I will strive to make sure both happen in my
classroom. This year I am teaching geometry and finite/trig.
This is my (23 +22+21+20)th year of teaching, but only my (32)th year at Kennedy. I have
taught every math class from algebra through calculus, starting in the year (2*103)-3. I
worked at Santa Monica High School and Birmingham High School before coming to
Kennedy. I have had many of you or your older siblings/cousins in previous classes and
am looking forward to knowing each of you better throughout the year!
Key: [ ] means greatest integer function
You are only eligible for extra credit if you are present on Friday 11/22 and Monday 12/2
and get at least 3 out of 4 on the homework assignment from Friday 11/22.
To earn 4 points extra credit: print out and translate Mrs. Jones’s mathography.
To earn an additional 10 points extra credit: write your own mathography in math code
and provide answers on a different page. Turn in everything on Monday 12/2.
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McDougal Honors Geometry chapter 6 notes
6.1 Ratios, proportions, and the geometric mean
Day 1: Read section 6.1 and take notes on pg 356-359. Do guided practice 1-11 all.
Day 2: Pg 360 #7-71 odds.
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6.2 Use proportions to solve geometry problems, pg. 367 #3-37 odds
TK#50: Properties of proportions
The geometric mean of 2 positive numbers a and b is the positive number x such that
a x
 . So x2=ab and x  ab.
x b
1.
Cross product property. In a proportion, the product of the extremes equals the
product of the means. If
2.
Reciprocal property. If 2 ratios are equal, then their reciprocals are also equal.
If
3.
a c
 where b≠0 and d≠0, then ad=bc.
b d
a c
b d
 , then  .
b d
a c
If we swap the means of a proportion, then we form another true proportion. If
a c
a b
 , then  .
b d
c d
4.
In a proportion, if we add the value of each ratio’s denominator to its
numerator, then we form another true proportion. If
ab cd

.
b
d
a c
 , then
b d
Guided practice 1-4.
Example 5.
(If time) Prove: If
a c
ab cd
 , then

.
b d
b
d
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6.3 Use similar polygons, pg 376 #5-33 odds, 36, 39 (on graph paper)
2 polygons are similar (~) if corresponding angles are congruent and corresponding
sides are proportional. If ABCD~EFGH, then corresponding angles are congruent:
A  E , B  F , C  G, D  H and corresponding sides are
AB BC CD DA



. In writing the similarity statements, order is
proportional:
EF FG GH HE
crucial!
B
F
A
D
E
G
H
C
TK#51: Similar polygons
Any corresponding 1-dimensional part (length, perimeter, etc) of similar polygons is
equal to the scale factor.
Guided practice 1,4-6.
__________ Quiz Review pg. 380 #1-7
__________Quiz 6.1-6.3. Hwk: Activity on the top of pg 381: Angles and similar
triangles (need protractor and ruler). Steps 1-4. Draw conclusions 1,2.
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6.4 Prove triangles similar by AA, pg 384#3-29 odds, 30-36E
Turn in Activity 6.4.
TK#52: AA similarity postulate: If 2 angles in one triangle are congruent to 2 angles in
another triangle, then the 2 triangles are similar. Since J  X , K  Y , then
∆JKL~∆XYZ by AA∆~Post.
K
Y
L
Z
X
J
Guided practice 2, 4.
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6.5 Prove triangles similar by SSS and SAS
TK#53: SSS Similarity Thm: If all 3 corresponding sides of two triangles are
proportional, then the triangles are similar. If
AB BC CD


, then ∆ABC~∆RST
RS ST TR
by SSS∆~ Thm.
A
R
C
T
S
B
TK#54: SAS Similarity Thm: If 2 sides of one triangle are proportional to the
corresponding 2 sides of another triangle and the included angles are congruent, then the
two triangles are similar. If
JK KL

and K  Y , then ∆JKL~∆XYZ by
XY YZ
SAS∆~ Thm.
K
Y
L
Z
X
J
Find x to make ∆JKL~∆MYZ
Example
K
3(x-2)
Y
12
L
21
Z
x+6
20
30
M
J
Guided practice 1-3.
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If time: prove guided practice 4.
Prove the SSS∆~ Thm.
6.5 one day: pg 391 #3-37 odds or 6.5 day 1 pg 391 #3-27 odds, 35, 39-44 (bring
compass and straightedge tomorrow)
6.5 day 2 pg 393 #18-34E, 37, 38 (bring compass and straightedge tomorrow)
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6.6 Use proportionality thms
TK#55: Triangle Proportionality Thm: If a line parallel to one side of a triangle
intersects the other 2 sides, then it divides the 2 sides proportionally. If TU || QS , then
RT RU

.
TQ US
Q
T
R
S
U
TK#56: Converse of Triangle Proportionality Thm: If a line divides 2 sides of a triangle
proportionally, then it is parallel to the third side. If
RT RU

, then TU || QS .
TQ US
TK#57: Extended Proportionality Thm: If 3 parallel lines intersect 2 transversals, then
they divide the transversals proportionally.
r
s
t
Y
U
V
UW VX

WY
XZ
l
W
X
Z
m
TK#58: Angle Bisector Proportionality Thm: If a ray bisects an angle of a triangle, then
it divides the opposite side into the same proportion as the 2 sides that form the angle.
AD AC

DB BC
A
D
C
B
Example 4.
Guided practice 2, 3.
6.6 day 1 pg 400#3-19 odds, 22, 27 (need compass and straightedge)
6.6 day 2 pg 400#12-20E, 21, 23-25 (need compass and straightedge)
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Dilation Activity 6.7 on pg 408 Steps 1-4. Draw conclusions 1,2. (Need graph paper,
compass, and ruler.) Hwk: Ch 6 review pg 418 #2-18 all. Print out Ch 7 notes.
6.7 Perform similarity transformations (Need graph paper). Pg 412 #3-21 odds (skip 17)
Turn in Activity 6.7 and ch 6 review.
With dilation: If 0<k<1, reduction. If k>1, enlargement.
Guided practice 2, 3.
_______ Ch 6 Test, Collect TK#1-58.
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