Q.4 ABCD is a quadrilateral.

Is AB + BC + CD + DA > AC + BD?

Is AB + BC + CD + DA > AC + BD?

In \(\triangle \)ABC, we have

AB + BC > AC …(i)
[Sum of any two sides is greater than the third side]

In \(\triangle \)BDC, we have

BC + CD > BD …(ii)

In \(\triangle \)ADC, we have
CD + DA > AC .... (iii)

In \(\triangle \)DAB, we have
DA + AB > BD …(iv)

Adding eq. (i), (ii), (iii) and (iv), we get

2AB + 2BC + 2CD + 2DA > 2AC + 2BD

Or, AB + BC + CD + DA > AC + BD [Dividing both sides by 2]

Hence, proved