NCERT Class 9 Maths Chapter 7 Triangles Solutions
NCERT Class 9 Maths Chapter 7 Triangles Solutions Exercise 7.1 Q.1. In quadrilateral ABCD AC = AD and AB bisects ∠ A.Show that ∠ ABC≅∆ADB. What can you say about BC and BD? Ans: In ∆ABC and ∆ABD AC = AD (Given) ∠ CAB = ∠ DAB (Given) AB = AB (Given) Therefore, By SAS congruence condition ∆ABC ≅∆ABD So, BC = BD (By C.P.C.T) Q.2. ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ BCA Prove that (i) ∆ABD ≅ ∆ BAC Ans: In ∆ ABD and △BAC (ii) BD = AC Ans: AD = BC (Given) (iii) ∠ ABD =∠BAC Ans: ∠ DAB = ∠CBA (Given) (Common) and AB = BA By SAS Congruence Condition ∆ABD ≅ ∆BAC (ii) BD=AC( By C.P.C.T) (iii) ∠ABD = ∠ BAC (Again by C.P.C.T) Q.3. AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB. Ans: In ∆ AOD and ∆ BOC AD=BC (Given) ∠ OAD = ∠ OBC (each 90⁰) ∠ AOD = ∠ BOC (Vertically opposite angles) Therefore, by ASA congruence condition. So, OA = OB (By C.P. С.Т.)...