Question 1068274
<pre>
We use this theorem:

If the diagonals of a quadrilateral bisect each other, the 
quadrilateral is a parallelogram.

1. Draw a line 5.2 cm long. 

2. Open the compass to 1/2 the length
of the shorter diagonal (1/2 of 6cm is 3cm)

3. Placing the sharp point of the compass on the right end of the
line, and swing an arc (the one I have in green).

4. Open the compass to 1/2 the length
of the longer diagonal (1/2 of 6.4cm is 3.2cm)

5. Placing the sharp point of the compass on the left end of the
line, and swing an arc (the one I have in red).

{{{drawing(400(26/31),(2000/9)(26/31),-1,8,-1,4,

line(0,0,5.2,0), locate(2.4,0,5.2cm),
green(arc(5.2,0,6,-6,140,160)),
red(arc(0,0,6.4,-6.4,20,40)) )}}}

6. Draw a line 6cm long from the right end of the line through
the point where the arcs cross.

6. Draw a line 6.4cm long from the left end of the line through
the point where the arcs cross.

{{{drawing(400*26/31,(2000/9)(26/31),-1,8,-1,4,

line(0,0,5.2,0), 



locate(1.3,1.3,3.2cm), locate(3.4,1.3,3cm), 
locate(3.5,2.6,3.2cm), locate(1.5,2.6,3cm),

line(0,0,.2384615385+5.2,3.37389035),
locate(2.4,0,5.2cm),
line(5.2,0,.2384615385,3.37389035),
green(arc(5.2,0,6,-6,140,160)),
red(arc(0,0,6.4,-6.4,20,40)) )}}}

7. Draw in the other three sides of the parallelogram.

{{{drawing(400(26/31),(2000/9)(26/31),-1,8,-1,4,

line(0,0,5.2,0), 
line(0,0,.2384615385,3.37389035),
line(.2384615385,3.37389035,.2384615385+5.2,3.37389035),
line(.2384615385+5.2,3.37389035,5.2,0), line(5.2,0,0,0),
locate(1.3,1.3,3.2cm), locate(3.4,1.3,3cm), 
locate(3.5,2.6,3.2cm), locate(1.5,2.6,3cm),

line(0,0,.2384615385+5.2,3.37389035),
locate(2.4,0,5.2cm),
line(5.2,0,.2384615385,3.37389035),
green(arc(5.2,0,6,-6,140,160)),
red(arc(0,0,6.4,-6.4,20,40)) )}}}

Edwin</pre>