Question

32. ABCD is a quadrilateral in which AB = CD and AD = BC. Show that it is
a parallelogram.​

Answer 1

•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.