Question

which are similar to △abc?
choose 1 answer:
△def only
△igh only
both
neither

Explanation:

Step1: Check similarity for $\triangle DEF$

For $\triangle ABC$ with sides \(a = 4\), \(b = 6\), \(c = 7\) and $\triangle DEF$ with sides \(d = 9\), \(e = 12\), \(f = 7\).
\(\frac{4}{9}
eq\frac{6}{12}
eq\frac{7}{7}\) (ratios of corresponding sides not equal).

Step2: Check similarity for $\triangle IGH$

For $\triangle ABC$ and $\triangle IGH$ with sides \(a = 4\), \(b = 6\), \(c = 7\) and \(a'= 6\), \(b' = 9\), \(c'=10.5\).
\(\frac{4}{6}=\frac{2}{3}\), \(\frac{6}{9}=\frac{2}{3}\), \(\frac{7}{10.5}=\frac{2}{3}\) (ratios of corresponding sides equal).

Answer:

B. $\triangle IGH$ only