Question -
Answer -
Given : In the figure, ABCD is a quadrilateral and AC is joined
To prove :
(i) CD + DA + AB + BC > 2AC
(ii) CD + DA + AB > BC
Proof:
(i) In тИЖABC,
AB + BC > AC тАж(i)
(Sum of two sides of a triangle is greater than its third side)
Similarly in тИЖADC,
CD + DA > AC тАж(ii)
Adding (i) and (ii)
CD + DA + AB + BC > AC + AC
тЗТ CD + DA + AB + BC > 2AC
(ii) In тИЖACD,
CD + DA > CA
(Sum of two sides of a triangle is greater than its third side)
Adding AB to both sides,
CD + DA + AB > CA + AB
But CA + AB > BC (in тИЖABC)
тИ┤ CD + DA + AD > BC