ABCD is a rectangle in which diagonal BD bisects angle B.Show that a b c d is a square.


can I do it in this process

BD bisects angle B
therefore angle ABD =angle DBC

angle ABD = angle DBC( alternate angles)

each angle of rectangle is 90°
therefore ABD = 45°
similarly ADB=45°

therefore AB = AD therefore each angle is equal it is a square

Dear Student,

Please find below the solution to the asked query:

We form our diagram from given information , As :



Here , $\angle$ ABD  =  $\angle$ CBD  =  45$°$                   --------- ( 1 )        (  We know all angles of rectangle at 90$°$ )

And
$\angle$ CBD  =  $\angle$ ADB  =  45$°$                             --------- ( 2 )                ( Alternate angles as we take BC  | | DA and BD as transversal line )

From equation 1 and 2 we get ABD is isosceles triangle and from base angle theorem we get . 

AB  =  AD  , So

AB  =  BC  =  CD  =  AD 

Therefore,

ABCD is a square .                                                          ( Hence proved )


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