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ABCD is a quadrilateral prove that (AB+BC+CD+DA) >(AC+BD) |
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Answer» ong>Answer: Step-by-step EXPLANATION:ABCD is a quadrilateral and AC, and BD are the diagonals. SUM of the two SIDES of a TRIANGLE is greater than the third side. So, considering the triangle ABC, BCD, CAD and BAD, we get AB + BC > AC CD + AD > AC AB + AD > BD BC + CD > BD
Adding all the above equations,
2(AB + BC + CA + AD) > 2(AC + BD) ⇒ 2(AB + BC + CA + AD) > 2(AC + BD) ⇒ (AB + BC + CA + AD) > (AC + BD) HENCE, PROVED |
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