If in two triangle ABC and DEF, ∠A = ∠E, ∠B = ∠F, then which of the following is not true?

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).

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