Question

In the adjoining figure, ABCD is a quadrilateral
in which AD = BC and ZDAB
BC and ZDAB = ZCBA. Prove
that
(1) AABD = ABAC
(ii) BD = AC
(iii) ZABD = ZBAC.​

Answer 1

Answer:

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 ]