Transcript 4.4 - Mathmatuch

Do Now 1/6/14
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Copy HW in your planner.
 Text
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p. 166, #1-19 all, 23 &24
In your notebook, use cross products to tell
whether the ratios below are proportional (equal).
16, 40
6 15
3, 18
8 46
240 = 240;
equal
138 = 144;
not equal
8, 24
9 27
216 = 216;
equal
28 , 42
12 18
504 = 504;
equal
“Basic Geometry Concepts”
Point
position in space
represented by a dot.
A
L
D
Z
K
Plane
a flat surface that extends on
forever in all directions.
How many planes on this figure?
Line segment
part of a line with 2 endpoints
and all the points in between.
D
EF
FE
E
C
CD DC
F
Line
a straight path extending
without end in 2 directions.
R
S
ST
T
RT
RS
Ray
Part of a line that begins
at a point and extends in one
direction without ending.
B
A
A
K
AB
J
K
JK
Congruent
Two line segments are
congruent when they are the
same length.
C
3
CD  EF
EF  3
D
E
F
Angle
Two rays that begin at the
same point.
D
Sides
C
Vertex
E
Naming Angles

The following angle can be named in three ways:
B
C
A
BAC
CAB
Vertex
A
Objective

SWBAT use ratios to determine if two
figures are similar
Section 4.4 “Similar Figures”
Similar Figures
Two figures are SIMILAR FIGURES if they have
the same shape but not necessarily the same
size. The symbol ~ indicates two figures are
similar.
Two figures are similar if:
1). The measures of their corresponding angles are equal
2). The ratios of the lengths of their corresponding sides
are proportional (equal ratios)
Corresponding angles –
matching angles of two figures
ABC ~ DEF
When 2 angles have
the same measure,
they are marked with
the same symbol or
measurement.
A  D
C  F
D
35°
A
35°
120°
 B  E
E
25°
120°
B
C
25°
F
Corresponding sides –
matching sides of two figures
ABC ~ DEF
AB
AC BC


DE
EF
DF
D
A
F
E
C
B
Given ABC ~ XYZ, name the corresponding
angles and corresponding sides.
Z
A
X
Y
Angles
A  X ,
C
B
B  Y ,
C  Z
Sides
AB correspond s to XY ,
AC correspond s to XZ ,
CB correspond s to YZ
Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
E
AB corresponds to DE.
16 in
A 10 in C
28 in
BC corresponds to EF.
D
4 in
7 in
40 in
F
AC corresponds to DF.
B
AB ? BC ? AC
=
=
DE
EF
DF
4 ? 7 ? 10
=
=
16
28 40
? 1 ? 1
1 =
=
4
4
4
Write ratios using the corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are equivalent, the
triangles are similar.
Identify the corresponding sides in the pair of triangles.
Then use ratios to determine whether the triangles are
similar.
E
AB corresponds to DE.
9 in
8 in C
A
21 in
BC corresponds to EF.
D
3 in
7 in
32 in
F
AC corresponds to DF.
B
AB ? BC ? AC
=
=
DE
EF
DF
Write ratios using the corresponding sides.
3
9
Substitute the length of the sides.
? 7 ? 8
=
=
21 32
? 1 ? 1
1 =
=
4
3
3
Simplify each ratio.
Since the ratios of the corresponding sides are not equivalent,
the triangles are not similar.

With triangles, if the corresponding side lengths
are all proportional, then the corresponding
angles MUST have equal measures.

With figures that have 4 or more sides, if the
corresponding side lengths are all proportional,
then corresponding angles MAY or MAY NOT
have equal measures.
QRST ~ ABCD because
corresponding sides are proportional
and corresponding angles are equal.
ABCD is not similar to WXYZ
because corresponding sides are
proportional and but corresponding
angles are NOT equal.
Tell whether the figures are similar.
The corresponding angles of the figures have equal measure.
? OP =
? MP
? NO =
MN =
ST
QR
RS
QT
6? 8 ?
=
=
9 12
4 ? 10
6 = 15
? 2=
2=
? 2=
?2
3 3 3 3
Write ratios using corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
60 m
125°
90°
80 m
Tell whether the figures are
N similar.
M
60 m
80°
90°
N
P
100 m
65°
125°
80 m
Q
T
65°
240 m
O
O
400 m
80°
47.5 m
47.5 m
R
90°
125°
320 m
190 m
S
Q
T
400 m
The corresponding angles of the figures have equal measure.
80°
65°
?
240
mNO ? OP ? MP
190 m
MN
= corresponding
=
= using
Write ratios
125°
90°
ST
QR
RS
QT
sides.
S
R
320 m
60 ? 80 ? 47.5 ? 100
240 = 320 = 190 = 400
? 1? 1 ? 1
1=
= =
4 4
4 4
Write ratios using corresponding sides.
Substitute the length of the sides.
Simplify each ratio.
Since the ratios of the corresponding sides are
equivalent, the figures are similar.
Try it out
Tell whether the figures are similar.
119°
59°
59°
35°
107°
55°
86°
86°
35°
107°
80°
79°
135°
38°
NP ? NO ? PO
=
=
QS
QR RS
7 ? 4 ? 6
=
=
14
12
8
? 1 ? 1
1 =
=
2
2
2
Similar
Not similar;
corresponding
angles do not have
equal measures