Exercise 11 Page 434

Practice makes perfect

a Recall that two polygons are similar if and only if the two following conditions are met.

All corresponding angles are congruent.
All pairs of corresponding sides are proportional.

We are told to assume corresponding angles are congruent, so we only have to determine whether the second statement is true. Let's check if the ratio of the shorter sides of the air hockey table and the hockey rink is equal to the ratio of their longer sides. Note that 85feet=1020 inches and 200feet=2400 inches.

Shorter Sides	Longer Sides
40.8in./1020in.	96in./2400in.
1/25	1/25

The ratios are equal. Since the air hockey table and the hockey rink are rectangles, we have enough information to conclude that the surfaces are similar.

b From Part A we know that the air hockey table and the hockey rink are similar. Therefore, we will find the ratio of their perimeters and the ratio of their areas. Let's start by determining the scale factor k of the hockey rink to the air hockey table.

k=40.8in./85ft=40.8in./1020in.=1/25 We have that k=125. It means that the hockey rink is 25 times as large as the air hockey table. Recall that when two similar polygons have a scale factor of k, the ratio of their perimeters is k and the ratio of their areas is k^2. &Ratio of Perimeters & & Ratio of Areas [0.7em] & 1/25 & & (1/25)^2=1/625

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Exercise 11 Page 434

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