Post on 01-Apr-2015
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