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ABCD is a quadrilateral with diagonals AC and BD. Which statement is true?

Class 7Triangle InequalityTriangles
  • AAB + BC + CD + DA < AC + BD
  • BAB + BC + CD + DA > AC + BD
  • CAB + BC + CD + DA = AC + BD
  • DAC + BD > 2(AB + BC)

Step-by-Step Solution

Triangle ABC: AB + BC > AC. Triangle ACD: CD + DA > AC. Triangle ABD: AB + DA > BD. Triangle BCD: BC + CD > BD. Adding all four: 2(AB + BC + CD + DA) > 2(AC + BD).
Answer: B) AB + BC + CD + DA > AC + BD

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