| Which pairs of triangles in the given figure are similar? |
 |
A) (i) and (ii)
B) (ii) and (iii)
C) (i) and (ii)
D) None of these
Correct Answer: C
Solution :
| Here \[\frac{AB}{DF}=\frac{4}{6}=\frac{2}{3}\], \[\frac{BC}{EF}=\frac{5}{7.5}=\frac{2}{3}\], |
| \[\frac{AC}{DE}=\frac{3}{4.5}=\frac{2}{3}\] |
| As, \[\frac{AB}{DF}=\frac{BC}{EF}=\frac{AC}{DE}\] |
| So, \[\Delta ABC\tilde{\ }\Delta DFE\] |
| [by SSS similarity criterion] |
| Hence, figures (i) and (ii) are similar triangles, but no other pairs of triangles in the given figure are similar. |
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