Question

ABCD is a quadrilateral in which ab is equal to CD and AD is equal to BC show that it is a parallelogram​

Answer 1

Step-by-step explanation:

In quadrilateral ABCD , we have

AB=CD and AD=BC .

Now join segment AC.

Now in ,ΔABC and ΔACD, we have

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

AD=BC ---------------- already given and

AC=AC ---------------- common

Hence

ΔABC≡ΔACD

∴∠DAC=∠BCA - both opposite equal sides DC andAB , 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.

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