Question

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

• A. ABC
• B. AEF
• C. BFD, CDE
• D. AFE, BFD, CDE

Answer 1

Answer: (B), (C), (D)

The correct options are
B

AEF

C

BFD, CDE

D

AFE, BFD, CDE

Consider $△AEF$
AE = AF (As $△ABC$ is equilateral and E and F are midpoints of sides AC and AB respectively)
$\Rightarrow \angle AFE=\angle AEF=\angle A={60}^o$
$\Rightarrow △AEF$ is equilateral.

Similarly we can prove that $△DEC$ and $△BFD$ are equilateral.
Since $△DEF$ share a common side with each of the other three triangles, $△DEF$ is also equilateral.

$\Rightarrow △DEF\cong △AEF$
$\Rightarrow △DEF\cong △DEC$
$\Rightarrow △DEF\cong △BFD$ by using SSS postulate.