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Question

Through the vertex D of a parallelogram ABCD, a line is drawn is the sides BA and BC produced at E and F respectively then DAAE=FBBE=FCCD

A
True
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B
False
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Solution

The correct option is A True
In DCF and EAD
2=1(corresponding angles)
and 4=3(corresponding angles)
by using AA similar condition,
DCFEAD
DCEA=CFAD=DFED
DCEA=CFAD
DCCF=EAAD
CFDC=ADEA .......(1)
Now, in EAD and EBF
1=1(common)
and 3=4(corresponding angles)
by using AA similar condition
EADEBF
EAEB=ADBF=EDEF
EAEB=ADBF
ADAE=BFBE .......(2)
Comparing (1) and (2), we get
DAAE=FBBE=FCCD
Hence the given statement is true.

1494206_1059349_ans_47d95b5437a14006820658f8838e41d9.PNG

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