Question

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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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..