Question

1)
a) similar
b) similar
c) similar
d) not so
2)
a) similar
b) not similar
the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.
3)
a) 5:6
b) 8:9
c) 3:5
d) 1:5
4)
a) 7:8
b) 1:2
c) 1:3
d) 1:5
the polygons in each pair are similar. find the missing side length.
5)
a) 11
b) 30
c) 9
d) 18

Explanation:

Step1: Determine scale factor for problem 3

For similar polygons, scale factor is ratio of corresponding sides. Take \(40\) and \(48\) (or \(48\) and \(54\)). \(\frac{40}{48}=\frac{5}{6}\) (simplify by dividing numerator and denominator by \(8\)).

Step2: Determine scale factor for problem 4

Take \(3\) and \(9\) (corresponding sides). \(\frac{3}{9}=\frac{1}{3}\) (simplify by dividing numerator and denominator by \(3\)).

Step3: Find missing side for problem 5

Set up proportion using similar polygons. \(\frac{16}{24}=\frac{6}{x}\) (cross - multiply: \(16x = 6\times24\)). Then \(x=\frac{6\times24}{16}=\frac{144}{16} = 9\).

Answer:

1. A. \(5:6\)
2. C. \(1:3\)
3. C. \(9\)