Question:
If in two triangle $\mathrm{ABC}$ and $\mathrm{DEF}, \angle \mathrm{A}=\angle \mathrm{E}, \angle \mathrm{B}=\angle \mathrm{F}$, then which of the following is not true?
(a) BCDF=ACDE
(b) ABDE=BCDF
(c) ABEF=ACDE
(d) BCDF=ABEF
Solution:
In ΔABC and ΔDEF
$\angle \mathrm{A}=\angle \mathrm{E}$
$\angle \mathrm{B}=\angle \mathrm{F}$
$\therefore \triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar triangles.
Hence $\frac{\mathrm{AB}}{\mathrm{EF}}=\frac{\mathrm{BC}}{\mathrm{FD}}=\frac{\mathrm{CA}}{\mathrm{DE}}$
Hence the correct answer is (b).