Geometry 7.3 Similar Polygons. Similar Figures This is the same figure scaled differently. Each of...
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Transcript of Geometry 7.3 Similar Polygons. Similar Figures This is the same figure scaled differently. Each of...
![Page 1: Geometry 7.3 Similar Polygons. Similar Figures This is the same figure scaled differently. Each of the…](https://reader035.fdocuments.in/reader035/viewer/2022062601/5a4d1bf27f8b9ab0599e6817/html5/thumbnails/1.jpg)
Geometry
7.3Similar Polygons
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Similar FiguresThis is the same figure scaled differently. Each of the figures is proportional to the other two.
~
The symbol for SIMILAR is~
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Similar vs. Congruent•The word similar has a specific
meaning in Geometry.Congruent figures have:•the same shape•the same size
Similar figures have:•the same shape•can be different sizes
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Similar PolygonsTheir vertices can be paired so that:•Corresponding angles are congruent•Corresponding sides are in proportion
(their lengths have the same ratio)
4 8
6
12
84
3
6
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Order is important
A
B
C
DE
M
N
O
PQ
ABCDE ~ MNOPQ
m<A = m<Mm<B = m<N
m<C = m<Om<D = m<P
m<E = m<Q
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Are the polygons similar? Why or why not?
No. Congruent angles, but sides not proportional
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No. Proportional sides (they are the same), but angles are not congruent
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Are the polygons similar? Why or why not?
Yes. Congruent angles and proportional sides
40
504
3
5
6
8 10
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Sometimes, Always, Never SimilarTwo rectangles: ______ Two scalene triangles: _____Two equilateral triangles: ______ Two rhombuses: _____A right triangle and isosceles triangle: ______ A square and a rhombus: ___
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ABCDEFA’B’C’D’E’F’ABCDEF ~ A’B’C’D’E’F’Find the following:a. Scale Factor: ________b. The values of v, x, y, z:
c. Perimeters of two hexagons: d. Ratio of the perimeters:
A
B C
D
EF
A’
B’ C’
D’
E’F’
ABCDEF ~ A’B’C’D’E’F’
3012
y12
15
z
208
6x
v
18
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A B
CD
A’ B’
C’D’
ABCD ~ A’B’C’D’
y
30 22
50
x
12
z
30 Scale factor: ________
Values of x, y, z : ________
The ratio of the perimeters: ________
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Homeworkpg. 250 CE #1-10
WE #1-27Makeups tomorrow after schoolQuiz Thursday
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130
60
Find m<B, m<Y, m<D and m<Z.
AB
CD
W X
Y
Z
m <B = m <X = 60m <Y = m <C = 130m <A = m< W = 90
m < D = 360 – (90 + 60 + 130)m < D = 360 – 280
m < D = 80 = m < Z
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EXAMPLE:
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Scale Factor• If two polygons are similar, then the ratio of
the lengths of two corresponding sides is called the scale factor.
Scale factor is
24
6
1213
= = 13
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Quad ABCD ~ Quad A’B’C’D’ (read A prime, B prime, etc.)Find the:(a) scale factor(b) values of x, y and z(c) perimeters of the two quadrilaterals(d) ratio of the perimeters
1020
8x
z
30
21
y
DD’
C
C’
B B’A A’
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1020
8x
z
30
21
y
DD’
C
C’
B B’A A’
Scale factor: DCD’C’
= 2030
= 23
23
=x21
x = 14
23
= 8y
y = 12
23
= 10z
z = 15
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1020
814
15
30
21
12
DD’
C
C’
B B’A A’
Perimeter of quad ABCD is 10 + 20 + 8 + 14 = 52
Perimeter of quad A’B’C’D’ is 15 + 30 + 12 + 21 = 78
Ratio of perimeters is 5278
= 23
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From the homeworkpg. 250 #1-4pg. 251 #26