Here, BC || DE, AB || EF and AC || DF
Remember: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
Therefore, the quadrilaterals BCAD,= ABFC and ABCE are parallelograms.
In the parallelogram BCAD,
BC = AD....(1)
Remember:Opposite sides of a In the parallelogram ABCE,
BC = AE … (2) parallelogram are equal.
Adding (a) and (b), we have
2BC = AD + AE = DE
Similarly, DF = 2AC and EF = 2AB
Hence, statement 1 is correct.
In ΔABD and ΔABC
AD = BC (Opposite sides of a parallelogram are equal)
BD = AC (Opposite sides of a parallelogram are equal)
AB = AB (Common)
∴ ΔABD = ΔABC(SSS congruence rule)
⇒ar(ΔABD)=ar(ΔABC)
Similarly, ar(ΔABC)=ar(ΔACE) and ar(ΔABC)=ar(ΔBCF)
∴ar(ΔABC)=ar(ΔDEF)⇒ ar(ΔDEF)=4×ar(ΔABC)
Hence, statement 2 is correct