Question

In the given figure, ABCD is a parallelogram. Prove that $AB=2BC$

Answer 1

Let draw a line parallel to both lines BC and AD

now in $△AEOand△ADE\frac{AE}{AO}=\frac{AE}{AD}$ (by Thales's theorm)

$\Rightarrow AO=AD=BC$

similarly in$△CBEand△OBC\frac{EB}{BC}=\frac{EB}{OB}$ (by Thales's theorm)

$\Rightarrow OB=BCOA+OB=BC+BC\Rightarrow AB=2BC$

Proved