Question
Mathematics Question on Congruence of Triangles
ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that
(i) ∆ ABD ≅ ∆ BAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.
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)