7-1B Similar PolygonsWhat is a proportion?

What are proportions used for in Geometry?What Geometry symbol is used for “is similar to”?

What similar figure is used for travel?

Definition

• Proportion--an equation stating that two ratios are equal.

32

128

gal1mi

gal10mi300 x

Geometry Symbols

The symbol ~ means “is similar to”. The order of the letters in the similarity correspondence indicates the corresponding parts.

ABC ~ XYZ

ABCDE ~ MNOPQ. Name all pairs of congruent corresponding angles, and write proportions using the pairs of corresponding sides.

QEPDOCNBMA

,,

,,:Angles

QMEA

PQDE

OPCD

NOBC

MNAB

lengthsSide

A

BC

D

E

M

N O

P

Q

Write the similarity correspondence. Name all pairs of congruent corresponding angles and write proportions using the pairs of corresponding sides.

JIHEFG ~HGIFJE ,,

21

HJGE

IHFG

JIEF

YXWVQRST ~

WSXRYQVT

,,,

3VYTQ

WVST

XWRS

YXQR

E

F

G3

4

537°

H

I

J

6

8

1053°

Q R

ST

45

60 75

90WV

XY 1520 25

30

Map Reading

The scale on a map relates the size of an object on the map to its actual size.

Where do you find the scale on a map?Use the scale and algebra to find the distance

between Mishawaka and Kokomo.

Given: FGHJ~WXYZFind YZ

Since the length of the corresponding sides are proportional, set up a proportional statement.

YZHJ

WXFG

YZ14

129

3218

91214

YZ

F

G

H

J9

14

W

X

Y

Z12

EFGH ~ KNML• Find the measures of angles E, G, and N.• Find x, y, and z.• What is the similarity ratio of KNML to EFGH?

67Em

E

F

GH

10143°

43°

46

X

K

L M

N

10

35

y

z67°

107°

x = 14, y = 15, z = 25

107Gm 43Nm

5/2

• What is a proportion?A proportion is an equation stating that two ratios

are equal.• What are proportions used for in Geometry?To find the length of the sides of similar figures.• What Geometry symbol is used for “is similar

to”? ~• What similar figure is used for travel?Maps

Assignment 7-1Bp. 471, 1-8, 11-13, 28-33