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Given That-AB||DC&AB=DC
To Prove-ΔABD≅ΔACB
Constuction-Join AC & BD
Proof- AB||DC (Given)
AB=DC (Given)
When a pair of side are equal and parallel then a quadrilateral is converted into a parallelogram
∴ABCD is a parallelogram
AD||BC (opposite sides of parallelogram are parallel )
AD=BC (opposite sides of parallelogram are equal)
AD=BC (proved above)
AB=DC (Given)
BD=DB (Common sides)
∴ΔABD≅ΔCDB (By SSS Congruence rule)
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