11. ABCD is a quadrilateral. Prove that AB + BC + CD + DA > AC + BD
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11. ABCD is a quadrilateral. Prove that AB + BC + CD + DA > AC + BD
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Answer:
2(AB + BC + CA + AD) > 2(AC + BD)
⇒ 2(AB + BC + CA + AD) > 2(AC + BD)
⇒ (AB + BC + CA + AD) > (AC + BD)
ABCD is a quadrilateral and AC and BC are the diagonals
sum of two sides of triangle is greater than three sides of triangle
has considering the triangle ABC D come and b c d and c a d and b a d we get
AB + BC > AC
CD + AD > AC
AB +AD > BC
BC + CD > BD
adding all three in the above equation
2(AB+ BC+CA+AD) > 2(AC+BD)
=> [ AB+BC+CA+AB] > 2( AC+BC)
I hope this would help you (⊙_⊙)