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ICSE Class 8 Answered

in parallelogram abcd,e is the midpoint of ad and f is the midpoint of bc.prove that bfde is a parallelogram 
Asked by rajankjose | 25 Aug, 2018, 04:03: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove space colon square BFDE space is space straight a space parallelogram.
Given space colon space square ABCD space is space straight a space Parallelogram.
left parenthesis straight i right parenthesis AD thin space equals space BC space and space AB thin space equals space CD.... left parenthesis opposite space sides space of space parallelogram space are space equal right parenthesis
left parenthesis ii right parenthesis AD parallel to BC space and space AB parallel to CD
AD space equals space BC space.... from left parenthesis straight i right parenthesis
rightwards double arrow 1 half AD space equals 1 half space BC space space...... left parenthesis iii right parenthesis
We space know space that space straight E space is space the space mid minus point space of space AD space and space straight F space is space the space mid minus point space of space BC.
rightwards double arrow AE thin space equals space ED space and space BF space equals space FC
form left parenthesis iii right parenthesis comma space we space get
rightwards double arrow AE space equals space ED space equals space BF space equals space FC space........ left parenthesis iv right parenthesis
In space space square BFDE comma
from left parenthesis left parenthesis iv right parenthesis
BF space equals space DE space space space space....... left parenthesis straight v right parenthesis
BF thin space parallel to space DE.... left parenthesis since comma space BC thin space parallel to space AD right parenthesis space space space.... left parenthesis vi right parenthesis
from left parenthesis straight v right parenthesis space and space left parenthesis vi right parenthesis
rightwards double arrow square BFDE space is space straight a space parallelogram.


end style
Answered by Yasmeen Khan | 27 Aug, 2018, 12:19: PM
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