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