5. Prove: Because Be is perpendicular to AC, DF is perpendicular to AC, and F and E are vertical feet,

So BE//DF, angle AEB= angle CFD=90 degrees,

Because the quadrilateral ABCD is a parallelogram,

So AD//BC, AD=BC,

So angle ACD= angle CAB,

Because angle AEB= angle CFD=90 degrees, angle ACD= angle CAB, AD=BC,

So the triangle ABE is equal to the triangle CDF(A, a, s),

So BE=DF,

Because BE=DF, BE//DF,

So the quadrangle BEDF is a parallelogram.

16. it is known that in quadrilateral ABCD, AD//BC, angle B+ angle C= 180 degrees,

It is proved that the quadrilateral ABCD is a parallelogram

It is proved that because angle B+ angle C= 180 degrees,

So AB//DC,

Because from AD 100 to BC 100, DC,

So the quadrilateral ABCD is a parallelogram.

17. Guess: EF and GH are equally divided.

It is proved that because the quadrilateral ABCD is a parallelogram,

So AD//BC, AD=BC,

Because AD=BC, AE=FC,

So ED=BF,

Because AD//BC, AE=FC = fc,

The quadrilateral AFCE is a parallelogram,

So AF//EC,

Because AD//BC, ED=BF = BF,

The quadrilateral BFDE is a parallelogram,

So BE//FD,

Because AF//EC, BE//FD,

The quadrilateral EGFH is a parallelogram,

So EF and GH are equally divided.