ABCD is a parallelogram.E and F are centroids of trangles ABD and BCD respectively,what will EF be equal to and how? AE BE CE DE YOU MUST BE KNOWING THE ANSWER BY MCQ METHOD,BUT PLEASE CAN YOU SHOW THE METHOD ALSO,PLEASE.
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Answer:AE
solution:
we know that,centroid of a triangle is the point of intersection of the medians of a triangle .And also centroid of a triangle divides each median in the ratio 2:1.
Then,we get,
AE/OE=2/1 and CF/OF=2/1
AE=2OE......1. and. CF=2OF..............2
we know diagonals of a parallelogram bisect each other.
Therefore,AO=OC
AE+OE=CF+OF
By eq1 and eq2 we get,
2OE+OE=2OF+OF
3OE=3OF
OE=OF........................3
similarly we can prove,
AE=CF.........................4
by eq1,eq2,eq3,eq4 we get,
AE=2OE=2OF=CF..................5
now,we have
OE+OF=OE+OE. (by eq3)
EF=2OE
EF=AE. (by eq 5)
solution:
we know that,centroid of a triangle is the point of intersection of the medians of a triangle .And also centroid of a triangle divides each median in the ratio 2:1.
Then,we get,
AE/OE=2/1 and CF/OF=2/1
AE=2OE......1. and. CF=2OF..............2
we know diagonals of a parallelogram bisect each other.
Therefore,AO=OC
AE+OE=CF+OF
By eq1 and eq2 we get,
2OE+OE=2OF+OF
3OE=3OF
OE=OF........................3
similarly we can prove,
AE=CF.........................4
by eq1,eq2,eq3,eq4 we get,
AE=2OE=2OF=CF..................5
now,we have
OE+OF=OE+OE. (by eq3)
EF=2OE
EF=AE. (by eq 5)
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