Transcript 7.3 Similar Polygons

Geometry
7.3
Similar Polygons
Similar Figures
~
This 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 Polygons
Their vertices can be paired so that:
• Corresponding angles are congruent
• Corresponding sides are in proportion
(their lengths have the same ratio)
12
6
4
4
8
8
3
6
Order is important
N
B
M
A
O
C
E
D
ABCDE
~
Q
P
MNOPQ
m<A = m<M
m<C = m<O
m<B = m<N
m<D = m<P
m<E = m<Q
Are the polygons similar? Why or why not?
105
80
No.
Congruent
angles, but
sides not
proportional
No. Proportional
sides (they are
the same), but
angles are not
congruent
Are the polygons similar? Why or why not?
4
40
5
10
8
50
6
3
Yes.
Congruent
angles and
proportional
sides
Sometimes, Always, Never Similar
Two rectangles:
______
Two equilateral triangles:
______
A right triangle and isosceles triangle: ______
Two scalene triangles: _____
Two rhombuses:
_____
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:
18
F
20
E
8
F’ 30 E’
z
12
A
D
A’
D’
v
6 15
y
B’
C’
B
C
x
12
ABCDEF ~ A’B’C’D’E’F’
50
D
C
22
30

Scale factor:
________
A
30
D’
x
A’

Values of x, y, z : ________

The ratio of the perimeters: ________
B
y
12
C’
z
B’
ABCD ~ A’B’C’D’
Homework
pg. 250
CE #1-10
WE #1-27
Makeups tomorrow after school
Quiz Thursday
EXAMPLE:
Find m<B, m<Y, m<D and m<Z.
C
D
Z
130
130
60
B
Y
60
A
W
X
m <B = m <X = 60
m < D = 360 – (90 + 60 + 130)
m <Y = m <C = 130
m < D = 360 – 280
m <A = m< W = 90
m < D = 80 = m < Z
Scale Factor
• If two polygons are similar, then the ratio
of the lengths of two corresponding sides
is called the scale factor.
6
2
4
=
= 1
3
12
Scale factor is
1
3
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
D’
D
20
C
10
A
30
z
y
8
x
B
C’
A’
21
B’
D’
D
20
x
Scale factor:
3
=
y
8
A
2
C’
z
C
10
30
B
DC
D’C’
x
2
21
3
x = 14
=
=
20
30
B’
21
A’
=
2
3
8
2
y
3
y = 12
=
10
z
z = 15
D’
D
20
C
10
A
30
15
12
8
14
B
C’
A’
B’
21
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
52
78
=
2
3
From the homework
pg. 250 #1-4
pg. 251 #26