Q5 of 63 Page 156

If in a cyclic quadrilateral ABCD, AD || BC, then prove that ∠A = ∠D.

Given ABCD is a cyclic quadrilateral and AD || BC.



We have to prove that ∠A = ∠D.


Proof:


Since AD || BC and CD is a traversal.


So, ∠BCD + ∠ADC = 180° … (1)


But ABCD is a cyclic quadrilateral.


⇒∠BCD + ∠BAD = 180° … (2)


From (1) and (2),


⇒∠ADC = ∠BAD


∴ ∠D = ∠A


Hence proved.


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