ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF.
Hence ΔBEC≅ΔDCF.
State whether the above statement is true or false.
True
False
A
False
B
True
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Solution
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∠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, △FDC≅△CBE (SAS rule)
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