Question

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that δABD ≌ ΔBAC.

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Answer 1

Step-by-step explanation:

ABCD is a quadrilateral, where AD=BC and ∠DAB=∠CBA

In △ABD and △BAC,

⇒ AD=BC [ Given ]

⇒ ∠DAB=∠CBA [ Given ]

⇒ AB=BA [ Common side ]

∴ △ABD≅△BAC [ SAS Congruence rule ]

∴ ∠ABD=∠BAC [ CPCT ]

Answer 2

Step-by-step explanation:

Given:AD=BC

∠DAB=∠CBA

Prove:ΔABD≌ΔBAC

proof:AD=BC [Given]

∠DAB=∠CBA [Given]

AB=BA. [Common sides]

.°. ΔABD≌ΔBAC [SAS Congruence rule]