Question

In the figure alongside, given that AB = BE
and that BD = BC prove that AE is parallel to DC,​

Answer 1

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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