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.

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.

cdquestions Admin · Accepted 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)

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

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.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions