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Question

ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF.

Hence ΔBECΔDCF.

State whether the above statement is true or false.


  1. True
  2. False

A
False
B
True
Solution
Verified by Toppr

BAD=CDF (Corresponding angles for parallel lines AB and CD)
BAD=CBE (Corresponding angles for parallel lines AB and CD)
Thus, CDF=CBE (I)
We know, AD=BC (ABCD is a parallelogram)
and AD=DF (Given)
Thus, DF=BC (II)
Similarly, BE=CD (III)
Now, In CDF and CBE
CDF=CBE (From I)
FD=BC (From II)
BE=CD (From III)
Thus, FDCCBE (SAS rule)

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