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Step-by-step explanation:
Given:
ABCD is a parallelogram
DE is perpendicular to AC
BF is perpendicular to AC
Prove that : BEDF is a parallelogram
In Triangle ADE and Triangle BCF
Angle AED= Angle BFC [each 90]
Angle DAE= Angle BCF [Alternate angles]
AD= BC [Opposite sides of parallelogram]
Triangle AED= Triangle BCF (BY A. A. S)
Therefore DE= BF. [C. P. C. T. C]... (i)
Angle DEA= Angle BFC (each 90)
Therefore DE //BF
From (i) and (ii)
DE= BF & DE//BF
Therefore BEDF is a parallelogram
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