So AB//CD AB=CD
Because the two midpoints
So AE = be =1/2abdf =1/cd-be = df.
So the quadrilateral DEBF is a parallelogram (a set of opposite sides are parallel and equal).
And because AD= 1/2 AB.
So AD=AE
Because the angle DAB = 60
So the triangle ADE is an equilateral triangle.
So DE=AE=BE
So the quadrilateral DEBF is a rhombus (parallelogram with equal adjacent sides).
(2) The quadrilateral AGBD is rectangular because:
Because AD//CG, AG//BD
So the quadrilateral AGBD is a parallelogram (two groups of opposite sides are parallel respectively).
Because DE=BE, AE=DE
So angle ADE= angle DAB, angle BDE= angle ABD.
So angle ADE+ angle BDE= 1/2 (angle ADE+ angle BDE+ angle DAB+ angle ABD)=90.
The quadrilateral AGBD is a rectangle (a parallelogram with right angles).