Question

identifying similar figures determine whether the figures are similar. explain your reasoning. 6. 7.

Explanation:

Step1: Calculate the ratios of corresponding sides for problem 6

For the first figure (smaller one), \(AB = 3\) (from \(x = 1\) to \(x = 4\)), \(AD=1\) (from \(y = 2\) to \(y = 3\)). For the second - level figure (\(HB\)), \(HB = 3\) (from \(x = 2\) to \(x = 5\)), \(AH = 1\) (from \(y = 3\) to \(y = 4\)). For the largest figure (\(EF\)), \(EF=6\) (from \(x = 2\) to \(x = 8\)), \(AE = 3\) (from \(y = 3\) to \(y = 6\)). The ratios of corresponding horizontal sides: \(\frac{AB}{HB}=\frac{3}{3} = 1\), \(\frac{HB}{EF}=\frac{3}{6}=\frac{1}{2}\). Since the ratios of corresponding sides are not equal.

Step2: Calculate the ratios of corresponding sides for problem 7

For \(\triangle ABC\) and \(\triangle JKL\). \(AC = 2\) (from \(x = 0\) to \(x = 2\) for \(x\) - coordinate of \(C\) and \(A\)), \(AB=\sqrt{(2 - 0)^2+(2 - 2)^2}=\sqrt{4}=2\). \(JL = 4\) (from \(x = 2\) to \(x = 2\) and \(y = 2\) to \(y = 6\)), \(JK=\sqrt{(6 - 2)^2+(3 - 6)^2}=\sqrt{16 + 9}=5\), \(KL=\sqrt{(6 - 2)^2+(3 - 2)^2}=\sqrt{16+1}=\sqrt{17}\). Also, \(\angle A=\angle J = 90^{\circ}\). The ratio of \(AC\) to \(JL\) is \(\frac{AC}{JL}=\frac{2}{4}=\frac{1}{2}\). The ratio of \(AB\) to \(JK\) is \(\frac{AB}{JK}=\frac{2}{5}\). Since the ratios of corresponding sides are not equal.

Answer:

1. The figures are not similar because the ratios of their corresponding sides are not equal.
2. The figures are not similar because the ratios of their corresponding sides are not equal.