Ex 6.4, 5 - Chapter 6 Class 7 Triangle and its Properties

Transcript

Ex 6.4, 5 ABCD is a quadrilateral. AB + BC + CD + DA < 2 (AC + BD)?In ∆AOB, Sum of two sides > Third side ⇒ AO + BO > AB Similarly, In ∆BOC, BO + CO > BC In ∆COD, CO + DO > CD In ∆AOD, DO + AO > DA Adding (1), (2), (3), (4) AB + BO + BO + CO + CO + DO + DO + AO > AB + BC + CD + DA 2 AO + 2 BO + 2 CO + 2 DO) > 2 AB + BC + CD + DA 2 (AO + CO) + 2 (BO + DO) > AB + BC + CD + DA 2 AC + 2 BD > AB + BC + CD + DA 2 (AC + BD) > AB + BC + CD + DA AB + BC + CD + DA < 2 (AC + BD) Hence proved.