1

Monday 10/17/11 warm­up

Answer on your mini whiteboard

2

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

3

Working with a neighbor, discuss how can you solve these 6 questions?

DE is a midsegment of triangle ABC

4

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?

9

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

5

6.2 P367­369 #1­4, 11­14, 16­18, 22­27, 30

6

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?

7

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

10

8

12

12

5

4

6

6

Scale factor

Perimeters

8

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

32

58

9

6.3 p376­377 #1­4, 6­9, 14­20

6.4 p384­385 #1­14, 16

10

Wednesday 10/19 Warm­up

1 2

= ??

3

4

5

11

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

12

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

13

6.5 p391­393 #1­8, 10­12, 25­27

6.6 p400­401 #1­11, 13­17

14

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