6.2 – use proportions to solve geometry problems

6.2 – Use Proportions to Solve Geometry Problems

Property Result

Reciprocal Property

Interchange Means

Adding

,a c

If thenb d

=

,a c

If thenb d

=

a b c d

b d

+ +=

b d

a c=

a b

c d=

,a c

If thenb d

=

Complete the statement.

y

x=

107

?

?

7

10=If , then

y

x

?

?

24

6=If , then

x

y

Complete the statement.

yx

246=

?

?3=

+xxIf , then 9+y

y

Complete the statement.

yx

93=

?

?=

+yyx

If , then 5+1111

Complete the statement.

11

5=

yx

Use the given information and the diagram to find the unknown length.

1

x=

3x = 2

x =23

3

2

Use the given information and the diagram to find the unknown length.

3

4=

3x = 24

x = 8

6

x

Use the given information and the diagram to find the unknown length.

12

x=

18x = 180

x = 10

18

15

Use the given information and the diagram to find the unknown length.

12

9=

12x = 144

x = 12

16

x

6.3 – Use Similar Polygons

Similar Polygons:

• Corresponding angles are congruent

• Corresponding sides are proportional

Scale Factor:

The ratio of the lengths of two corresponding sides of similar figures.

List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.

=DE

AB

Angles

A D

B E

C F

Sides: =EF

BCDF

AC

List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.

=MJ

CD

Angles

C M

D J

E K

Sides: =JK

DE

ML

CF

F L

=KL

EF

Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor.

Angles

A F

B D

C E

Sides: =6

3

2

1

=10

5

2

1

=8

4

2

1

Yes, they are similar.

ABC ~

Scale factor:2

1

FDE

Angles

Q W

R X

S YT Z

Sides: =3

6

1

2

=6

8

3

4

No, they are not similar.

The polygons are similar as noted. Find the value of x.

6

4=

6x = 48

x = 8

12

x

The polygons are similar as noted. Find the value of x.

8

12=

8x = 144

x = 18

BCED ~ KLMJ12

x

The two triangles are similar. Find the values of the variables.

6

12=

6m = 66

m = 11

6

12=

12n = 48

n = 4

5.5

m 8

n

5. The two figures are similar. Find the scale factor of their sides. Then find the ratios of their perimeters. What do you notice?

18

6 4

12128

Scale Factor:12

8=

3

2

Ratio of Perimeters:36

24=

3

2

They are the same!

Ratios of Perimeters:

If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths

ratioperimeters

side

The ratio of one side of a picture to the corresponding side of a larger picture is 2:7. The perimeter of the smaller picture is 16 inches. Find the perimeter of the larger picture.

2

7=

2x = 112

x = 56in

2

7

16x

16

x

In the diagram, MNOP ~ WXYZ .

a.Find the scale factor of MNOP to WXYZ .

5

4

10

8=

In the diagram, MNOP ~ WXYZ .

b. Find the values of x, y, and z.

5

4=

4x = 60

x = 15

5

4=

5y = 40

y = 8

z° = 135°12

x 10

y

In the diagram, MNOP ~ WXYZ .

c. Find the perimeter of MNOP.

10 + 15 + 10 + 15

50

d. Find the ratio of the perimeter of MNOP to the perimeter of WXYZ.

In the diagram, MNOP ~ WXYZ .

12 + 8 + 12 + 8

40

PerimeterMNOP

PerimeterWXYZ=

5

4

50

40=

HW Problem

6.3 # 12

Ans:

6.2

6.3

367-369

376-378

3-11 odd, 12, 16-18, 28, 29

3, 7-12, 19, 20, 31, 32

36in5

3=

60x