CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 7. Similarity

Solution:This is an example of anextendedproportion. Substituting in the numbers for the sides we know, we have
4
XY=

3

9 =

AC

15. Separate this into two different proportions and solve forXYandAC.

4

XY

=

3

9

3

9

=

AC

15

36 = 3 (XY) 9 (AC) = 45

XY= 12 AC= 5

Example 8:In the picture,EDAD=BCAC. Findy.

Solution:Substituting in the numbers for the sides we know, we have

6

y

=

8

12 + 8

.−→ 8 y= 6 ( 20 )

y= 15

Example 9:IfABBE=CDACin the picture above, findBE.

Solution:

12

BE

=

20

25

−→ 20 (BE) = 12 ( 25 )

BE= 15

Know What? RevisitedEverything needs to be scaled down by a factor of 181 ( 144 in÷ 8 in). Change everything
into inches and then multiply by the scale factor.

Bed: 36 in by 75 in−→2 in by 4.167 in

Desk: 48 in by 24 in−→2.67 in by 1.33 in

Chair: 36 in by 36 in−→2 in by 2 in

There are several layout options for these three pieces of furniture. Draw an 8 in by 8 in square and then the
appropriate rectangles for the furniture. Then, cut out the rectangles and place inside the square.

Review Questions

1. The votes for president in a club election were: Smith : 24 Munoz : 32 Park : 20 Find the following
   ratios and write in simplest form.