In the figure alongside, given that AB = BE
and that BD = BC prove that AE is parallel to DC,
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Step-by-step explanation:
we can prove this by SAS similarity criterion.
i.e.
(BE/BD)=(BA/BC). {given}
also, <EBA = <CBD. {vertically opposite angle}
So by SAS similarity criterion
EBA is similar to DBC
so <CDB = <AEB
<DCB = <EAB
As they form vertically opposite angle,
AE and CD are Parallel.
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