Lesson 9-6

Example 1	Find Measures of Similar Figures
The figures are similar.  Find each missing measure.

a.

The corresponding sides are proportional.

 = 	Write a proportion.
    = 		Replace BC with 9, EF with 15, AC with 12, and DF with x.
 9  x = 15  12	Find the cross products.
    9x = 180	Simplify.
	x = 20		Mentally divide each side by 9.

A

B

C

D

W

X

Y

Z

b.  

12

d

The scale factor that relates ABCD to WXYZ is or .  Use the scale factor to relate dimensions in WXYZ, x, to dimensions in ABCD, y.

y = kx		Direct variation equation
d = (12)		Substitute.
d = 8		Multiply.
Example 2	Use Indirect Measurement
MAPS	In the figure, GHK  JIK.  Find the distance across the forest.

The scale factor that relates GHK to JIK is or .
   y 	= kx			Direct variation equation
       18	= x			Substitute. 
   8(18) = 3x			Multiply each side by 8.
     = x			Divide each side by 3.
       48 = x			

The distance across the forest is 48 miles.		

Example 3	Use Shadow Reckoning
BUILDING	A large office building casts a 150-foot shadow at the same time a nearby pedestrian casts a 3 foot shadow.  If the pedestrian is 6 feet tall, how tall is the office building?

Explore	You know the lengths of the shadows and the height of the pedestrian.  You need to find the height of the office building.

Plan	Write and solve a proportion.

Solve	   =   	
	     		          6  150 = h  3		Find the cross products.
	          			   900 = 3h		Multiply.
	          			   300 = h		Mentally divide each side by 3.

The height of the office building is 300 feet.

Check	The pedestrian’s height is 2 times the length of his or her shadow.  The height of the office building should be 2 times the length of its shadow, or 2 · 150, which is 300 feet.