13. E and F are the mid-points of the sides AB and CD respectively of the parallelogram
ABCD
In each of the following, if the statement is true, give reasons:
(1) DF = EB
(ii) AF = EC
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8th
Maths
Understanding Quadrilaterals
Parallelogram
In a parallelogram ABCD,E a...
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Asked on December 26, 2019 by
Shilpa Pandiyan
In a parallelogram ABCD,E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.
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ANSWER
ABCD is ∥gm
AB∥CD
AE∥FC
⇒AB=CD
2
1
AB=
2
1
CD
AE=EC
AECF is ∥gm
In △DQC
F is mid point of DC
FP∥CQ
By converse of mid point theorem P is mid point of DQ
⇒DP=PQ (1)
∴AF and EC bisect BD
In △APB
E is mid point of AB
EQ∥AP
By converse of MPT ( mid point theorem )
Q is mid point of PB
⇒PQ=QB (2)
By (1) and (2)
⇒PQ=QB=DP
AF and EC bisect BD..
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