abcd is a quad and bd is one of its diagonals as shown in the fig. show that abcd is a parallelogram and find its area

Dear Student,

Please find below the solution to the asked query:

Here , $\angle$ ABD  = $\angle$ CDB  =  90$°$ 

If we take two lines AB and CD and BD as transversal line , So $\angle$ ABD  and $\angle$ CDB  are interior alternate angles .

And these angles are equal ( As given $\angle$ ABD  = $\angle$ CDB  =  90$°$ ) only when AB  | | CD . So

AB  | |  CD

And

AB  =  CD  =  3 cm 

We know if in a quadrilateral a pair of sides are equal and parallel to each other so that quadrilateral is a parallelogram .

So,

ABCD is a parallelogram                                                     ( Hence proved )

We know area of parallelogram  = Base $\times$ Height , So

Area of parallelogram ABCD  = AB $\times$ BD  =  3 $\times$ 4  =  12 cm²                             ( Ans )

Hope this information will clear your doubts about Areas of Parallelograms and Triangles.

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