Transcript Chap. 6-2 notes

Ch 6.2
• Similar polygons- polygons
have same shape but
different size
– Corresponding angles are
congruent
– Measure of corresponding
sides are proportional
– EX: ABCD ~ EFGH
Congruent <‘s Corresponding
Proportional Sides
<A
<B
<C
<D
≅
≅
≅
≅
AB = BC = CD = DA
EF
Symbol for similar ~
ABCD ~ EFGH
Ch 6.2
Congruent <‘s Corresponding
Proportional sides
<A
<B
<C
<D
≅ <E
≅ <F
≅ <G
≅ <H
AB = BC = CD = DA
EF FG GH HE
***If two polygons are
congruent they are also
SIMILAR
Symbol for similar ~
ABCD ~ EFGH
Ex 1: Determine whether each pair of
figures is similar. Justify your answer.
Ask yourself, what angles
are congruent and why?
Are the sides proportional?
** pay attention to corresponding
order
Sides opp 90 Sides opp 30 Sides opp 60
Are these triangles similar?
YES
AB =
DE
BC =
CA =
Ex 2:Determine whether each pair of
figures is similar. Justify your answer.
Ask yourself, what angles
are congruent and why?
Are the sides proportional?
** pay attention to corresponding
order
AB = and BC =
Are these rectangles similar?
Are these sides proportional?
Ex 2:Determine whether each pair of
figures is similar. Justify your answer.
Ask yourself, what angles
are congruent and why?
Are the sides proportional?
Are these rectangles similar?
NO
** pay attention to corresponding
order
AB = 7 = 1.166 and BC = 6= 1.2
EF 6
FG 5
Are these sides proportional?
NO
Scale Factor
• When you compare the lengths of
corresponding sides of similar figures, you
usually get a numerical ratio (i.e. FRACTION).
• The ratio is called the scale factor of the two
figures.
• Scale factors are often given for models of
real-life objects.
Scale Factor con’t
When finding the scale factor for two
similar polygons, the scale factor will
depend on the order of comparison.
The scale factor of quad ABCD to quad
EFGH is 2
AB = BC = CD = DA
EF FG GH HA
7 =2
3.5
The scale factor of quad EFGH to quad
ABCD is ½
EF = FG = GH = HE
AB BC CD DA
3.5 = 1
7
2
Ex 3: Some special effects in movies are created using miniature models. In a
recent movie, a model sports-utility vehicle (SUV) 22 inches long was created
to look like a real 14 2/3 foot SUV. What is the scale factor of the model
compared to the real SUV?
Scale factor = model
real
• Before finding the scale factor, make sure the measurements use the
same unit of measure.
Model = ____ = ____
Real
The ratio comparing the two lengths is ___ or
__:__. The scale factor is ___, which means the
model is ____ the length of the real SUV.
Ex 3: Some special effects in movies are created using miniature models. In a
recent movie, a model sports-utility vehicle (SUV) 22 inches long was created
to look like a real 14 2/3 foot SUV. What is the scale factor of the model
compared to the real SUV?
Scale factor = model
real
• Before finding the scale factor, make sure the
measurements use the same unit of measure.
x 12 in = 176 in
1 ft
Model = __22 in__ = 1
Real
176 in
8
(14 2/3 ft )
The ratio comparing the two lengths is 1/8 or 1:8 The scale
factor is 1/8 , which means the model is 1/8 the length of the
real SUV.
Ex 4: The two polygons are similar. Write a similarity
statement. Then solve for x, y, and UT.
• Use the congruent
angles to write the
corresponding vertices
in order.
Poly ______ ~ Poly ______
Ex 4: The two polygons are similar. Write a similarity
statement. Then solve for x, y, and UT.
Poly RSTUV ~ Poly ABCDE
Write proportions to find x and
y.
To find x
To find y
ST = VR
ST = UT
BC
BC
UT =
What is the scale factor for
poly RSTUV to poly ABCDE?
Ex 4: The two polygons are similar. Write a similarity
statement. Then solve for x, y, and UT.
Poly RSTUV ~ Poly ABCDE
Write proportions to find x and y.
To find x
To find y
ST = VR
ST = UT
BC EA
BC DC
18 = x
4
3
3(18) = 4x
54 = 4x
13.5 = x
18 = y+2
4
5
4(y+2) = 18(5)
4y + 2 = 90
4y = 88
y = 22
UT = y + 2 = 24
What is the scale factor for poly RSTUV to
poly ABCDE?
EX: 4 What is the scale factor for poly
RSTUV to poly ABCDE?
• The scale factor is the ratio of the length of
any two corresponding sides.
ST = 18 = 9
BC 4
2
EX: 5 Triangle ABC is similar to ⍍ XYZ with scale factor of 2/3. If the lengths
of the sides of ⍍ABC are 6, 8, and 10 inches, what are the lengths of the
sides of ⍍XYZ?
• Draw a picture
• Write proportions for finding side measures.
AB 
XY 
BC 
YZ
CA
ZX
The lengths of the sides of ⍍XYZ are _________________ inches.
EX: 5 Triangle ABC is similar to ⍍ XYZ with scale factor of 2/3. If the lengths
of the sides of ⍍ABC are 6, 8, and 10 inches, what are the lengths of the
sides of ⍍XYZ?
• Draw a picture
• Write proportions for finding side measures.
AB  6 = 2
XY  x
3
BC  8 = 2
YZ
y 3
CA 10 = 2
ZX z
3
The lengths of the sides of ⍍XYZ are
9, 12, and 15 inches.