Known AD=5,? BC= 12, the radical number 2 of DC=4, and e is the midpoint of BC.
(1) As shown in the left figure, FC=DF=4 (Pythagorean theorem), EC=BE=6, then EF=EC-FC=6-4=2.
In Rt△EFD, Germany? =DF？ +EF？ , get the root number 5 with DE=2.
AD≠DE。 Therefore, a quadrilateral cannot be a diamond.
(2) As shown in the right figure, DF=FC=4 (Pythagorean theorem), EF=EC-FC=6-4=2.
Let EP=5. In Rt△DFP, according to Pythagorean theorem, DP=5.
Because AD=DP=5, AD∨BC, that is, AD∨EP, quadrilateral AEPD is a parallelogram, because DP=DP=5, parallelogram AEPD is a rhombus (a group of parallelograms with equal adjacent sides are rhombus).