Question

If in ΔABC and ΔDEF, $\frac{AB}{DE}=\frac{BC}{FD}$, then they will be similar, when _________.

Answer 1

In ΔABC and ΔDEF, $\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}$.

Two triangles are similar if their corresponding sides are proportional.

∴ ΔABC $~$ ΔDEF when $\frac{\mathrm{AB}}{\mathrm{ED}}=\frac{\mathrm{BC}}{\mathrm{DF}}=\frac{\mathrm{CA}}{\mathrm{FE}}$.

If in ΔABC and ΔDEF, $\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}$, then they will be similar, when $\underline{\frac{\mathrm{AB}}{\mathrm{ED}}=\frac{\mathrm{BC}}{\mathrm{DF}}=\frac{\mathrm{CA}}{\mathrm{FE}}}$.