In `squareABCD, AB` is the smallest and CD is the largest side. Prove that :
(i) `angleB gt angleD` (ii) `angleA gt angle C`

Explanation

(i) join BD.
In `DeltaABD`
`A gt AB" "( :' AB" is smallest side")`
`implies" "angle ABD gt angleADB` ...(1)
In `DeltaBCD`
`CD gt BC" "( :' CD" is largest side")`
`angleCBD gt angleBDC` ...(2)
Adding equations (1) and (2)
`angleABD+angleCBD gt angleADB+angleBDC`
`angleABC gt angleADC`
`implies" "angleB gt angleD`
(ii) Join AC
In `DeltaABC`
`BC gt AB" "( :' AB" is smallest side")`
`angleBAC gt angleACB` ...(1)
In `DeltaACD`
`CD gt AD" "( :' CD" is largest side")`
`implies" "angleCAD gt angleACD` ...(2)
Adding equations (1) and (2)
`angleBAC+angleCAD gt angleACB+angleACD`
`implies" "angleBAD gt angleBCD`
`implies" "angleA gt angle C`