ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that - Mathematics
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
(i) ΔABD ≅ ΔBAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.
In ΔABD and ΔBAC,
AD = BC (Given)
∠DAB = ∠CBA (Given)
AB = BA (Common)
∴ ΔABD ≅ ΔBAC (By SAS congruence rule)
∴ BD = AC (By CPCT)
And, ∠ABD = ∠BAC (By CPCT)
Concept: Criteria for Congruence of Triangles
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