Question

ABCD is a quad. in which AB = CD and AD = BC ? Show that it is a //gm .

Answer 1

Please see below.

Explanation:

In quadrilateral `ABCD`, we have `AB=CD` and `AD=BC`.

Now join segment `AC`.

Now in `DeltaABC` and `DeltaACD`, we have

`AB=CD` ---------------- already given

`AD=BC` ---------------- already given

and `AC=AC` ---------------- common

Hence `DeltaABC-=DeltaACD`

`:./_DAC=/_BCA` - both opposite equal sides `DC` and `AB`, and

`:.CD`||`AB` - as alternate angles are equal

`:./_DCA=/_CAB` - both opposite equal sides `AD` and `BC`

`:.AD`||`BC` - as alternate angles are equal

As opposite sides of quadrilateral are parallel,

`ABCD` is a parallelogram.

`Q.E.D.`