Use Proportions to Solve Geometric Problems

6.2

Proportion Properties

• The Reciprocal Property:– If two ratios are equal, then their

reciprocal is also equal.

– Basically, you can flip ratios to make new equivalent ratios.

Examples

If , then 147

6 x

x

14

6

7

Proportion Properties

• If you have 2 ratios equal to each other, then the numerators can be turned into a new ratio and the denominators into another new ratio.

Examples

Proportion Properties cont.

• You can add the denominator of each ratio to the numerator to get a new ratio.

Examples

True or False?true

true

false

true

True or False?false

true

true

true

True or False?false

true

true

BA = 12, BD = x – 3 = 12 – 3 = 9

What do I know?

XW = 1, XY = 3, YZ = 2, and WV is unknown so WV = x

2

3

x

1 1(2) = 3x 2 = 3x

x3

2

SR = 3, RQ = 4, ST = 6, and TU = x

x

6

4

3

)4(63 x 243 x 8x

BC = x, AB = 12, CD = 24, and DE = 18

18

24

12

x )24(1218 x 28818 x16x

HI = 21, GH = 14, JK = x, and KD = 12

1214

21 x )12(2114 x 25214 x 18x

301218 KDJKJD

Worksheet