Question

In quadrilateral ABCD, AB || CD and AD || BC. Prove that ZABC = ADC.​

Answer 1

Given :

AB||CD

ADIIBC

prove that angle ADC-ABC

prove:- ABIICD(given)

ADI|BC(given) Draw AC diagonal

AABC and AADC

AD=BC (opposite side)

AB=CD (opposite side)

AC-AC( common side)

AABC congruence AADC (S.S.S) therefore. angle ABC= angle ADC

Hence PROVED.

Answer 2

Given :

AB||CD

ADIIBC

prove that angle ADC-ABC

prove:- ABIICD(given)

ADI|BC(given) Draw AC diagonal

AABC and AADC

AD=BC (opposite side)

AB=CD (opposite side)

AC-AC( common side)

AABC congruence AADC (S.S.S) therefore. angle ABC= angle ADC

Hence PROVED.