Lesson 1: Similar Polygons - Side Lengths Example 2


EXAMPLE 2

Are the polygons below similar?

Solution


At first glance, the polygons look different because they are facing different directions.

Step 1: Redraw one of the polygons so they both have the same orientation.



Step 2: Determine all corresponding side length ratios.

relative position Polygon WXYZ Corresponding side on
Polygon TSRP 		Side length Ratio of
PRST:WXYZ
WX TS \(\frac{\text{ST}}{\text{WX}}=\frac{50}{20}\)

ratio = 2.5
XY SR \(\frac{\text{RS}}{\text{XY}}=\frac{55}{22}\)

ratio = 2.5
YZ RP \(\frac{\text{PR}}{\text{YZ}}=\frac{40}{15}\)

ratio = 2.666...
ZW PT \(\frac{\text{PT}}{\text{WZ}}=\frac{30}{12}\)

ratio = 2.5

Because the corresponding side length ratio for RP : YZ differs from the other ratios, the polygons are not similar.

   Points to Ponder

Once you determine that one corresponding side length ratio differs from another, no further calculations are required. This difference alone proves the two polygons are not similar. However, it is always best to verify your work to ensure the ratios are set up and calculated correctly.


Now, it is your turn! Complete the questions in your Chapter 8, Lesson 1 Practice Makes Perfect that refer to Side Lengths 2.



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