If a - b - c - d- the according to dividendo property a -b - b - c -d - d-a - b - a- c - d - c-a - b - b - c - d - d-a -b - a- c -d - c-

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Componendo and Dividendo Property

If a : b = c ...

Question

If a : b = c : d, the according to dividendo property

a + b : b = c + d : d

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a - b : a = c - d : c

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a - b : b = c - d : d

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a + b : a = c + d : c

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Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

(a) AB + BC + CD > AD;

(b) AB + BC + CD + DA > 2AC;

(d) AB + BC + CD + DA > AC + BD.

If (a + b +c + d) (a -b- c+ d)

=(a + b- c- d) (a -b+c- d);

prove that : a : b =c : d.

S = [\begin{matrix} a & b \\ c & d \end{matrix}]

[\begin{matrix} - d & - b \\ - c & a \end{matrix}]

[\begin{matrix} d & - b \\ - c & a \end{matrix}]

[\begin{matrix} d & b \\ c & a \end{matrix}]

[\begin{matrix} d & c \\ b & a \end{matrix}]

If a : b = c : d, the according to dividendo property

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