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