ABCD is a quadrilateral in which AD = BC and DAB = CBA : Prove that: 1. ABD BAC 2. BD = AC 3. ABD= BAC

In quadrilateral ACBD, we have AD = BC and ∠ DAB = ∠ CBA 1. In ∆ ABC and ∆ BAC, AD = BC (Given) ∠DAB = ∠CBA (Given) AB = AB (Common) ABD BAC ...[By SAS Congruence] 2. Since ∆ABD ≅ ∆BAC ⇒ BD = AC [By C.P.C.T.] 3. Since ∆ABD ≅ ∆BAC ⇒ ∠ABD = ∠BAC [By C.P.C.T.]

ABCD is a quadrilateral in which AD = BC and DAB = CBA : Prove th…

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Question

ABCD is a quadrilateral in which AD = BC and $\angle$DAB = $\angle$CBA : Prove that:

$\triangle$ ABD $\cong$ $\triangle$ BAC
BD = AC
$\angle$ ABD= $\angle$ BAC

✓

Answer

In quadrilateral ACBD, we have AD = BC and ∠ DAB = ∠ CBA

In ∆ ABC and ∆ BAC,
AD = BC (Given)
∠DAB = ∠CBA (Given)
AB = AB (Common)
$\triangle$ABD $\cong$ $\triangle$BAC ...[By SAS Congruence]
Since ∆ABD ≅ ∆BAC
⇒ BD = AC [By C.P.C.T.]
Since ∆ABD ≅ ∆BAC
⇒ ∠ABD = ∠BAC [By C.P.C.T.]