# Prove that EF is parallel to AB and CD in part (iii) using intercept theorum?

## Dear student,

I am giving a solution for c first part as your question is not clear and for the remaining parts kindly ask in another thread

$Weknowthatthelengthofthelinesegmentjoiningthemid-pointsof\phantom{\rule{0ex}{0ex}}twonon-parallelsidesishalfthesumofthelengthsofparallelsides.\phantom{\rule{0ex}{0ex}}\because EandFaremid-pointsofADandBC.\phantom{\rule{0ex}{0ex}}\therefore EF=\frac{1}{2}(AB+CD)\phantom{\rule{0ex}{0ex}}Now,giventhat-\phantom{\rule{0ex}{0ex}}AB=6cm\phantom{\rule{0ex}{0ex}}DC=4cm\phantom{\rule{0ex}{0ex}}\therefore EF=\frac{1}{2}(6+4)=5cm.\phantom{\rule{0ex}{0ex}}$

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