Transcript similar polygons

LESSON 8.2: SIMILAR
POLYGONS
OBJECTIVES:
 To identify similar polygons
 To apply similar polygons
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Similar Figures
have the same shape,
Similar figures ________________
but not necessarily the same size.
___________________________,
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Similar Polygons
Two polygons are similar if and only if
 ALL their NOTE:
corresponding
angles are
Both conditions
congruent must be met for two
polygons to be determined
AND
to be similar.
 ALL their corresponding sides are
proportional (equal ratios).
The mathematical symbol for similarity is
is similar to
________ and is read “___________.”
:
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UNDERSTANDING SIMILARITY
Given: V ABC : V XYZ
“is similar to” V XYZ
Read: V ABC ______________
ALL corresponding
angles
A   _____
X
 _____

B   _____
Y
 _____
C   _____
Z
 _____
ALL corresponding
sides proportional
BC = ___
___
AB = ___
AC
XY YZ
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XZ
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DETERMINING SIMILARITY
Is ABCD similar to JKLM?
Recall: BOTH conditions
must be met for two
polygons to be determined
to be similar.
Recall:
Consecutive angles of a
Opposite angles of a
supplementary
are _________________.
congruent
are _____________________.
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USING SIMILAR FIGURES
Given:
V ABC : V YXZ.
Find the value of x.
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Sketch ∆ XYZ and ∆ MNP with
 X   M ,  Y   N,  Z   P.
Recall: BOTH conditions
Label XY = 12,
YZbe= met
14, ZX
= 16, MN = 18,
must
for two
polygons
NP = 21, and
PM = to
24.be determined
to be similar.
Determine whether
the two triangles are similar.
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The Golden Ratio
A golden rectangle is
a__________________________
rectangle that can be divided
__________________________
into
a square and a rectangle that
is similar to the original
___________________________
__________________________.
rectangle.
The golden ratio is
__________________________
the ratio, length: width, in a
__________________________.
golden rectangle, 1.618: 1
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USING THE GOLDEN RATIO
KEY: Length = 1.618
Width
1
The dimensions of a
rectangular tabletop are
in the Golden Ratio.
The shorter side is 40
inches. Find the longer
side. Use a calculator.
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FINAL CHECKS FOR UNDERSTANDING
1. If two polygons are similar,
must they also be
congruent? Explain.
2. Find the values of a and
b, given that the two
polygons are similar.
3. Now, list ALL pairs of
congruent angles and
ALL pairs of proportional
sides.
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Homework:
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