Are the triangles in figure 1.56 similar? If yes, by which test?
Figure: \(\triangle PQR\) with PQ = 6, QR = 8, PR = 10 and \(\triangle LMN\) with LM = 3, MN = 4, LN = 5.
Answer: Yes, \(\triangle PQR \sim \triangle LMN\) by the SSS test of similarity.
Compare the corresponding sides:
\[\frac{PQ}{LM} = \frac{6}{3} = 2,\quad \frac{QR}{MN} = \frac{8}{4} = 2\] \[\frac{PR}{LN} = \frac{10}{5} = 2\]All three ratios of corresponding sides are equal, so the sides are in proportion.
Hence, by the SSS test, \(\triangle PQR \sim \triangle LMN\) (P ↔ L, Q ↔ M, R ↔ N).
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