6.2 – use proportions to solve geometry problems

6.2 – Use Proportions to Solve Geometry Problems

Property Result

Reciprocal Property

Interchange Means

Adding

,a cIf thenb d

,a cIf thenb d

a b c db d

b da c

a bc d

,a cIf thenb d

Complete the statement.

yx

107

??

710

If , then yx

??

246

If , then xy

Complete the statement.

yx246

??3

xxIf , then 9+y

y

Complete the statement.

yx93

??

yyxIf , then 5+11

11

Complete the statement.

115

yx

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

1x

3x = 2

x = 23

32

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

34

3x = 24

x = 8

6x

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

12x

18x = 180

x = 10

1815

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

129

12x = 144

x = 12

16x

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.

DEAB

AnglesA DB EC F

Sides: EFBC

DFAC

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

MJCD

AnglesC MD JE K

Sides: JKDE

MLCF

F L

KLEF

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

AnglesA FB DC E

Sides: 63

21

105

21

84

21

Yes, they are similar.

ABC ~

Scale factor:21

FDE

AnglesQ WR XS YT Z

Sides: 36

12

68

34

No, they are not similar.

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

64

6x = 48

x = 8

12x

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

812

8x = 144

x = 18

BCED ~ KLMJ12x

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

5.5m

6m = 66m = 11

612 8

n

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

5.5m

6m = 66m = 11

12n = 48n = 4

612 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: 128

32

Ratio of Perimeters:3624

32

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.

27

2x = 112x = 56in

2

7

16x

16x

7. In the diagram, WXYZ ~ BCDE.

a.Find the scale factor of WXYZ to BCDE.

64

32

7. In the diagram, WXYZ ~ BCDE.

b. Find the values of XY and YZ.32

3XY

6YZ

2XY = 9

XY = 4.5

4.5 4.5

7. In the diagram, WXYZ ~ BCDE.

b. Find the values of XY and YZ.32

3XY

6YZ

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

6.26.3

367-369376-378

3-11 odd, 12, 16-18, 28, 293, 7-12, 19, 20, 31, 32

x = 36in

53

60x

35

x60