Q9 of 63 Page 145

The vertices of quadrilateral ABCD lie on a circle such that AB = CD. Then prove that AC = BD.


Given AB = CD.


Construction:


Join AD and BC.


Consider ΔABC and ΔBCD,


⇒ AB = CD [Given]


⇒ ∠ABC = ∠BCD [Vertically opposite angles are equal]


⇒ BC = BC [Common side]


By SAS congruence rule,


⇒ ΔABC ≅ ΔBCD


By CPCT,


⇒ AC = BD


Hence proved.


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