Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 4-5

Example 1 Identify Similar Polygons
Determine whether rectangle QUAD is similar to rectangle LMNO. Explain.

First, check to see if corresponding angles are congruent.

Since the two polygons are rectangles, all of their angles are right angles. Therefore, all corresponding angles are congruent.

Next, check to see if corresponding sides are proportional.

Since  are not equivalent ratios, rectangle QUAD is not similar to rectangle LMNO.

Example 2 Find Missing Measures
Given that polygon QRST ~ polygon WXYZ, find m.
		
Method 1 Write a proportion.
The missing measure m is the length of . Write a proportion involving XY that relates corresponding sides of the two polygons.

 	XY = m, RS = 3, YZ = 10, and ST = 6.
	Find the cross products.
  15 = 3m	Multiply.
    5 = m	Divide each side by 3.

Method 2 Use the scale factor to write an equation.
Find the scale factor from polygon WXYZ to polygon QRST by finding the ratio of corresponding sides with known lengths.

scale factor:  or 		The scale factor is the constant of proportionality.

Words	A length on polygon WXYZ is  times as long as 
	a corresponding length on polygon QRST.

Variable	Let m represent the measure of .
	
Equation	m =   3
m =   3		Write the equation.
m = 5			Multiply.
Example 3 Standardized Test Practice Example
Triangle ABC is similar to triangle PQR. Each side of ABC is 2 times longer than the corresponding sides of PQR. If the perimeter of ABC is 76 inches, what is the perimeter of PQR?

A  190 in.	B  65 in.	C  30.4 in.	D  20.5 in.

Read the Test Item
Since each side of ABC is 2times longer than the corresponding sides of PQR, the scale factor from ABC to PQR is 2 or .

Solve the Test Item
Let x represent the perimeter of PQR. The ratio of the perimeters is equal to the ratio of the sides.
	Scale factor relating ABC to PQR
                               	Find the cross products.
                                  152 = 5x	Multiply.
                                  	Divide each side by 5.
                                  30.4 = x	Simplify.
The answer is C.