Question

ABCD is a quad , in which AB।।CD and AB= CD show that it is a ।।gm​

Answer 1

Answer:

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 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.