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Monday 10/17/11 warmup
Answer on your mini whiteboard
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Chapter 6 SimilarityYou will use the following skills from previous chapters again for chapter 6
• properties of parallel lines• using properties of triangles• simplifying expressions• finding perimeter
In this chapter you will learn the following terms:
• ratio• proportion• means/extremes• scale drawing• scale• similar polygons• scale factor of 2 similar polygons
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Working with a neighbor, discuss how can you solve these 6 questions?
DE is a midsegment of triangle ABC
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6.2 Use Proportions to Solve Geometry Problems
EQ: How can we use scale drawings to find real distances?
Vocabulary
Ratio
Proportion
means/extremes
Scale drawing
Scale
How can we solve a proportion?
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A
B C4
15
x
J
H N
EXAMPLE 1
EXAMPLE 2
S
T
K
M P
18
612
3
TS=?
TMMS = TP
PK
EXAMPLE 3
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6.2 P367369 #14, 1114, 1618, 2227, 30
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Tuesday 10/18 Warmup
1. Solve for x1528 =
9x
2. The map of Japan on the back wall has a scale of 1 : 5,300,000.If Tokyo and Kyoto are 6 cm apart on the map, how far are they apart in reality?
3. ΔABC≅ΔHPTIf AC = 21, which part of ΔHPT also = 21?
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6.3 Use Similar PolygonsEQ: If 2 figures are similar, how do you find the length of a missing side?
18 in
7 in
Vocab• Similar polygons
• Scale factor
46 in
???
W
Q
F
M
S
Y
H
L
Write a similarity statement
Corresponding angles
Ratio of corresponding sides
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8
12
12
5
4
6
6
Scale factor
Perimeters
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6.4 Prove Triangles Similar by AA
EQ: What is one way to prove triangles are similar?
What is the definition of similar triangles?
If you know the angle measures of 2 angles of a triangle, can you find the 3rd angle?
T
A
G
Postulate 22: AngleAngle Similarity Postulate
D
Y
M
BASIC
BEAUTIFUL EXAMPLES
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58
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6.3 p376377 #14, 69, 1420
6.4 p384385 #114, 16
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Wednesday 10/19 Warmup
1 2
= ??
3
4
5
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6.5 Prove Triangles Similar by SSS & SAS
EQ: How can side measures help us to prove triangles are similar?
Quick review:ratioproportionsimilar polygons
Theorem 6.2 SSS
Compare the ratios of the side lengths to see if they are similar
SHORT MEDIUM LONG SCALE FACTOR
Theorem 6.3 SAS
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6.6Use Proportionality TheoremsEQ: How can we use parallel lines and angle bisectors to make proportions?
Theorem 6.4 Triangle Proportionality Theorem & Theorem 6.5 (its converse)
Theorem 6.6
Theorem 6.7
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6.5 p391393 #18, 1012, 2527
6.6 p400401 #111, 1317
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5&6
5.15.25.35.4
5.5
6.2
6.36.4
6.56.6
5.5 p331332 #12, 612, 1626
5.3 p313314 #120 5.4 p322 #17, 9, 1315, 1722, 3335
5.1 p298300 #1, 311, 2426, 35 5.2 p306307 #19, 1115 odd
6.5 p391393 #18, 1012, 2527 6.6 p400401 #111, 1317
6.3 p376377 #14, 69, 1420 6.4 p384385 #114, 16
6.2 P367369 #14, 1114, 1618, 2227, 30