Question

ABCD is a quadrilateral. Prove that
$ab + bc + cd + da > ac + bc$


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Answer 1

In ∆ ABC,

AB + BC > AC...(1)

In ∆ ADC,

AD + CD > AC ....(2)

In ∆ ADB,

AD + AB > DB -(3)

In ∆ DCB,

DC+ CB > DB.(4)

Adding equation (1), (2), (3) and (4) we get,

AB + BC + AD + CD + AD + AB + DC+ CB > AC + AC + DB + DB

AB + AB + BC + BC + CD + CD + AD + AD > 2AC + 2DB

2AB + 2BC + 2CD + 2AD > 2AC + 2DB

AB + BC + CD + AD > AC + DB.

Answer 2

Answer:

ABCD is a quadrilateral which has four sides AB, BC, CD and DA, four angles ∠A,∠B,∠C and ∠D and four vertices A, B, C and D and also has two diagonals AC and BD. i.e. A quadrilateral has four sides, four angles, four vertices and two diagonals. Hence, ∠A + ∠B + ∠C + ∠D = 360o Proved. I.

Step-by-step explanation:

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