Question

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 1

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)