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

10

7

?

?

7

10If , then

y

x

?

?

24

6If , then

x

y

Complete the statement.

yx

246

?

?3

x

xIf , then 9+yy

Complete the statement.

yx

93

?

?

y

yxIf , then 5+11

11

Complete the statement.

11

5

y

x

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.

5.5

m

6m = 66

m = 11

6

12 8

n

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

5.5

m

6m = 66

m = 1112n = 48

n = 4

6

12 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

7. In the diagram, WXYZ ~ BCDE.

a.Find the scale factor of WXYZ to BCDE.

6

4

3

2

7. In the diagram, WXYZ ~ BCDE.

b. Find the values of XY and YZ.

3

2

3

XY

6

YZ

2XY = 9

XY = 4.5

4.5 4.5

7. In the diagram, WXYZ ~ BCDE.

b. Find the values of XY and YZ.

3

2

3

XY

6

YZ

2YZ = 18

YZ = 9

2XY = 9

XY = 4.5

4.5 4.5

9

7. In the diagram, WXYZ ~ BCDE.

c. Find mC.

mC = 117°

4.5 4.5

9

d. Find the perimeter of WXYZ.

7. In the diagram, WXYZ ~ BCDE.

4.5 4.5

99 + 4.5 + 4.5 + 6

24u

HW Problem

6.3 # 12

6.2

6.3

367-369

376-378

11, 12, 16, 17, 28, 29

3, 7-12, 19, 20

x = 36in

5

3

60

x

35

x60