Question

ABCD is a quadrilateral in which AD =BC and angle DAB =angle CBA . prove that ​

Answer 1

Question :-

ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see figure). Prove that

(i) ∆ABD ≅ ∆BAC

(ii) BD = AC

(iii) ∠ABD = ∠ BAC

Solution :-

In quadrilateral ACBD, we have

• AD = BC and
• ∠ DAB = ∠ CBA

(i) In ∆ ABC and ∆ BAC,

• AD = BC (Given)
• ∠DAB = ∠CBA (Given)
• AB = AB (Common)

∴ ∆ ABD ≅ ∆BAC (By SAS congruence)

(ii) Since ∆ABD ≅ ∆BAC

⇒ BD = AC [By C.P.C.T.]

(iii) Since ∆ABD ≅ ∆BAC

⇒ ∠ABD = ∠BAC [By C.P.C.T.]

hope it helps :)

Answer 2

$\huge\textrm{Answer:}$

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 ]