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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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Geometry
7.3Similar Polygons
Similar FiguresThis is the same figure scaled differently. Each of the figures is proportional to the other two.
~
The symbol for SIMILAR is~
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
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
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
Are the polygons similar? Why or why not?
No. Congruent angles, but sides not proportional
80105
No. Proportional sides (they are the same), but angles are not congruent
Are the polygons similar? Why or why not?
Yes. Congruent angles and proportional sides
40
504
3
5
6
8 10
Sometimes, Always, Never SimilarTwo rectangles: ______ Two scalene triangles: _____Two equilateral triangles: ______ Two rhombuses: _____A right triangle and isosceles triangle: ______ A square and a rhombus: ___
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
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: ________
Homeworkpg. 250 CE #1-10
WE #1-27Makeups tomorrow after schoolQuiz Thursday
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
60130
EXAMPLE:
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
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’
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
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
From the homeworkpg. 250 #1-4pg. 251 #26
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