Ex 6.4, 4 - Chapter 6 Class 7 Triangle and its Properties

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Ex 6.4, 4 ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?In ∆ABD, Sum of two sides > Third side ⇒ AB + DA > BD Similarly, In ∆BCD, BC + CD > BD In ∆ACB, AB + BC > AC In ∆ACD, CD + DA > AC Adding (1), (2), (3), (4) AB + DA + BC + CD + AB + BC + CD + DA > BD + BD + AC + AC 2 (AB + BC + CD + DA) > 2 (AC + BD) (2 (𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷 + 𝐷𝐴))/2 > (2 (𝐴𝐶+𝐵𝐷))/2 AB + BC + CD + DA > AC + BD Hence proved