Do Now 1/11/12Do Now 1/11/12

Take out your HW from last night.Take out your HW from last night. Text p. 166, #1-19 all, 23 &24Text p. 166, #1-19 all, 23 &24

Copy HW in your planner.Copy HW in your planner. Text p. 170, #1-11 all, 14-16 allText p. 170, #1-11 all, 14-16 all

In your journal, tell whether the figures are similar.In your journal, tell whether the figures are similar.

59°59°

35°35°

86°86°

119°

55°

107°

79°

107°

80°

135°

38°

Try it outTry it outTell whether the figures are similar.

59°59°

35°35°

86°86°

119°

55°

107°

79°

107°

80°

135°

38°

NPQS

=? NOQR

=? PORS

714

48

612

12

12

12

=? =?

=? =?

Similar Not similar; corresponding angles do not have equal measures

HomeworkHomework Text p. 166, #1-19 all, 23 &24Text p. 166, #1-19 all, 23 &24

1) similar 2) not similar 3) similar 4) not similar 5) not similar 6) similar 7) similar 8) not similar 9) No, corresponding angles are

not equal 10) 4 in. X 6 in., 16 in. X 24 in.

11) similar 12) not similar 13) yes 14) no 15) yes 16) yes 17) no 18) no 19) no 23) C 24) No

Objective

SWBAT use similar figures to find unknown measures

Section 4.4 “Similar Figures”Section 4.4 “Similar Figures”

Similar FiguresSimilar Figures

Two figures are Two figures are SIMILAR FIGURESSIMILAR FIGURES if they have the if they have the same shapesame shape but not necessarily the same size. The but not necessarily the same size. The symbol ~ indicates two figures are similar. symbol ~ indicates two figures are similar.

Two figures are similar if:Two figures are similar if:

1). The measures of their corresponding angles are equal 1). The measures of their corresponding angles are equal

2). The ratios of the lengths of their corresponding sides 2). The ratios of the lengths of their corresponding sides are proportional (equal ratios)are proportional (equal ratios)

28

8

x

12

42

3368

x

x

Cross Cross multiplymultiply

Section 4.5 “Using Similar Figures”

Given ABC ~ JKL, find x and y.Given ABC ~ JKL, find x and y.

KJ

AB

KL

BC

Angle B corresponds to Angle K

y = 103°

Given ABCD ~ GHIJ, find HJ.Given ABCD ~ GHIJ, find HJ.

GG HH

II JJ

AA BB

CC DD

30

12

x

16

GH

AB

HJ

BD

30

12

x

16

40

48012

x

x

Cross multiply

CC

AA

BB

bb

aa

3232 FF

DD

EE

2020

3535

4040

40

32

35

a

40

32

20

b

28

112040

a

a

16

64040

b

b

Given ABC ~ DEF, find a.Given ABC ~ DEF, find a.

Given ABC ~ DEF, find b.Given ABC ~ DEF, find b.

C

A

B

Y

Z

X

2020

gg

2525

2424 4040

ff

Given ABC ~ XYZ, find g and f.Given ABC ~ XYZ, find g and f.

XZ

AB

YZ

BC

XZ

AB

XY

AC

40

25

24

g

40

2520

f

15

60040

g

g

32

80025

f

f

Indirect Measurement Indirect Measurement

the method of using proportions to find an unknown length or distance in the method of using proportions to find an unknown length or distance in similar figuressimilar figures

Indirect MeasurementsIndirect Measurements

You measure the shadow of a telephone pole to be 24 ft. The shadow of a 5ft-tree is 4 ft. How tall is the telephone pole?

treeshadow

poleShadow

treeheight

poleHeight

SS

HH

ss

hh

30

1204

H

H

4

24

5

H

Indirect MeasurementsIndirect Measurements

To estimate the height of the Transco Tower in Houston, TX, you measure its shadow to be about 55m. The shadow of a 50m flagpole is about 10m. Estimate the height of the Transco Tower.

flagpoles

buildingS

flagpoleh

buildingH

SS

HH

ss

hh

275

275010

H

H

10

55

50

H

City officials want to know the height of a traffic light. Estimate the height of the traffic light.

27.2515

= 48.75h

Write a proportion.

27.25h = 731.25

The traffic light is about 27 feet tall.

27.25 ft

48.75 ft

h ft

Cross multiply.

h ≈ 27 ft Divide each side by 27.25 to isolate the variable.

Indirect MeasurementsIndirect Measurements

Homework

NJASK7 Prep

Text p. 170, #1-11 all, 14-16 allText p. 170, #1-11 all, 14-16 all