Question

ABCD is a quadrilateral in which AD = BC and ∟DAB = ∟CBA. Then prove that ∆ABD BAC and BD = AC​

Answer 1

Answer:

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 ]

Step-by-step explanation:

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Answer 2

Answer:

In △ABD and △BAC,

AD=BC (Given)

∠DAB=∠CBA (Given)

AB=BA (Common)

∴△ABD≅△BAC (By SAS congruence rule)

∴BD=AC (By CPCT)

And, ∠ABD=∠BAC (By CPCT)

Step-by-step explanation:

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