Question

how to construct parallelogram of two sides

Answer 1

Set the compass to the length of the left side, then move it so the spike rests at the bottom right corner. Draw another arc with the pencil, overlapping the first arc. Find the top right corner. The point where the two arcs cross is the top right corner of theparallelogram.

Answer 2

Hi, first of all remember that in a parallelogram the diagonals meet in their medium point. Stated this, if you want to construct your parallelogram you have to draw the given side AB. Then you draw two circles, the first with center A and radius d1/2, where d1 is the length of the first diagonal (in our case we get 10/2 = 5), the other with center B and radius d2/2, where d2 is the length of the second one (and here we get 5/2 = 2.5). Now, if the sum of the rays is < l (l = length of the given side) there is no parallelogram, if it is = l the parallelogram degenerates in a segment (the given side), if it is > l you can draw the parallelogram in the following way : the circle will meet in two distinct points. Choose one of them and call it M. Now draw two segments D1 with length d1 and D2 with length d2, both containing M, the first starting from A and the second from B. Their extremes will be the vertexes of the parallelogram. 
In our case we have d1/2+d2/2 = 5 + 2.5 = 7.5 cm, the length of the side, so the parallelogram is degenerate and constructing it simply means drawing the side. 
I hope I helped you