In Figure, `A B\ a n d\ C D` are respectively the smallest and longest sides of a quadrilateral `A B C Ddot` Show that `/_A >/_C\ a n d\ /_B >/_D`

Explanation

Given in quadrilateral ABCD,AB is the smallest and CD is the largest side
To find `angel B gt angle D or angle D gt angle B`
Construction join BD.
Now in `Delta ABD AD gt AB ` [since ,AB is the snallest side in ABCD ]

`rArr angle 1 gt angel 3 ` [angle opposite to larger side is greater ] ...(i)
` In Delta ABCD CD gt BC ` [ since ,CD is the largest side is grater ] ..(i)
` rArr angel 2 gt angle 4 ` [angle opposite to larger side is grater ]
On adding Eqs. (i) and (ii) we get
`angel 1 + angle 2 + gt angle 3 + angle 4`
Hence `angle B gt angle D`