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 –
Answer: Option A
:
B, C, and D
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B, C, and D
Consider △AEF
AE = AF (As △ABC is equilateral and E and F are midpoints of sides AC and AB respectively)
⇒∠AFE=∠AEF=∠A=60o
⇒△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.
⇒△DEF≅△AEF
⇒△DEF≅△DEC
⇒△DEF≅△BFD by using SSS postulate.
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