Transcript Stretching and Shrinking

Stretching and
Shrinking
Similarity
Similarity
Similar figures have the same shape
but not necessarily the same size.
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Tests for Similarity
• The measures of their corresponding
angles are equal.
• The lengths of their corresponding
sides increase by the same scale
factor.
MathScience Innovation Center © 2007
Question 1 - Review
Each of the shapes below have five
sides and 5 angles, but which
shape is similar to Z?
Z
1. Choice One
2. Choice Two A
3. Choice Three
B
ic
e
ho
C
C
ho
ic
e
Th
Tw
o
O
ic
e
ho
C
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re
e
0%
ne
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Question 2- Review
Triangle RST is an enlargement of
triangle WXY. Which answer
choice lists a pair of corresponding
S
sides?
X
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d
an
ST
an
ST
an
T
R
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d
XW
d
d
an
S
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Y
YW
W
XY
T
R
W
Y
RS and WY
RT and XW
ST and XY
ST and YW
R
1.
2.
3.
4.
Question 3 - Review
Triangle RST is an enlargement of
triangle WXY. Which answer
choice lists a pair of corresponding
S
angles?
XWY
Y
T
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d
0%
an
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d
0%
d
WYX
an
R
an
XWY
XYW
W
d
and
and
and
and
an
1. RST
2. RTS
3. STR
4. SRT
X
Question 4 - Review
If two figures are similar,
which of the following might be
different?
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a. number of sides
b. shape
c. size of angles
d. area
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Activity 1
The first shape is a self-similar shape
and the second is not. What do you
think a self-similar shape is?
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Question 1 – Activity 1
Is the number of copies of an
original shape used to make a
new shape related to the side
lengths or the area of the new
shape?
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1. Side lengths
2. Area of new shape
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Question 2 – Activity 1
Quad 1
Quad 2
Are these two quadrilaterals mathematically similar?
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o
Ye
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s
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N
1. Yes
2. No
Question 3 – Activity 1
Can the larger shape be divided
into smaller congruent shapes that
are similar to the original?
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o
Ye
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s
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N
1. Yes
2. No
YES
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Question 1 – Activity 2
What can be said about the
angles of similar figures
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1. The angles are different.
2. The angles are the same.
3. The angles change by 180°.
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Question 2 – Activity 2
Does the concept of similarity
apply to three dimensional shapes?
1. Yes
2. No
o
Ye
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s
Scale Models
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N
0%
Shrinking Cups
What would happen if you were
smaller?
What challenges would you face if
were much smaller, only inches tall?
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Shrinking Cups
What challenges would you face if
you had to design a cup to drink from
if you were only 6-12 inches tall?
Would we have to consider any
aspects other than size?
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