Question

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

Answer 1

Given:In □ABCD

AB=DCandAD=BC

To prove: ABCD is a parallelogram

Construction: Draw diagonal AC and DB.

Proof: in △ABC and △ADC

AD=BC [Given]

AB=DC [Given]

AC=AC [Common side]

∴ 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

Since AB∣∣DC and AD∣∣BC.

△ABCD is parallelogram