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Question

AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see figure). Show that A>C and B>D.
1472130_41d836bfb8b94c40892dddf3f460a2e9.jpg

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Solution

Construct two lines AC and BD in the given quadrilateral
Consider ABC
We know that BC>AB
It can be written as
BAC>ACB(i)
Consider ACD
We know that CD>AD
It can be written as
CAD>ACD(ii)
By adding both the equations we get
BAC+CAD>ACB+ACD
So we get
A>C
Consider ADB
We know that AD>AB
It can be written as
ABD>ADB(iii)
Consider BDC
We know that CD>BC
It can be written as
CBD>BDC(iv)
By adding both the equations we get
ABD+CBD>ADB+BDC
So we get
B>D.

1539809_1472130_ans_3e784f746eb24d38ad4eb63383594643.jpg

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