32. ABCD is a quadrilateral in which AB = CD and AD = BC. Show that it is
a parallelogram.
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•Given:
In □ABCD
AB=CD
AD=BC
•To prove:
ABCD is a quadrilateral
•Solution:
In ∆ABC and ∆ADC
AD=BC
AD=DC
AC=AC(Common)
∴ By SSS property
△ADC≅△ACB
∴∠DAC=∠DCA
∴AB∣∣DC [By theorem]
In△ABDand△DCB
DB=DB [Common side]
AD=BC [Given]
AB=DC [Given]
∴△ABD≅△DCB
∴AD∣∣BC
∴AD∣∣BCSince AB∣∣DC and AD∣∣BC.
△ABCD is parallelogram.
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