In the figure given below AC is parallel to BD, is AE/CE=DE/BE?.jystify your answer

Dear Student,

Please find below the solution to the asked query:

Given :  AC | | BD

In $∆$ AEC and $∆$ DEB

We take AD as transversal line , So

$\angle$ DAC = $\angle$ ADB                          ( Alternate interior angles )

$\angle$ EAC =  $\angle$ EDB                          ( As $\angle$ DAC = $\angle$ EAC and $\angle$ ADB=  $\angle$ EDB same angles )

And

$\angle$ AEC =  $\angle$ DEB                          ( vertically opposite angles )

So,
$∆$ AEC $~$ $∆$ DEB                         ( By AA rule )

And if we have two similar triangle then ratio of their corresponding side is equal , So

$\frac{\mathbf{AE}}{\mathbf{CE}}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{DE}}{\mathbf{BE}}$                               ( Hence proved )

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