## Task 5 - 010715

Can a parallelogram be constructed uniquely if the following are given:

a) two adjacent sides,

b) one side and two adjacent angles,

c) both diagonals,

d) one diagonal and the angles enclosed by the diagonals,

e) one diagonal and the two angles into which the corresponding angle of the parallelogram is divided by the diagonal?

How many pieces determine a parallelogram uniquely? Give 3 examples!
a) No, because, for example, both a rectangle and a parallelogram with any angle between the given sides can be constructed.

b) No, because the length of the other side is still freely selectable.

c) No, because the angle between the two diagonals is still freely selectable.

d) No, because the length of the second diagonal is still freely selectable.

e) Yes. Construction: Measure the length of the diagonal on a straight line, mark the given angles at both endpoints (alternate interior angles). The sides of the parallelogram lie on the resulting legs.

A parallelogram is uniquely determined by three pieces if these are not related by relationships such as the corresponding or alternate interior angles theorem.

One can imagine a parallelogram as two congruent triangles placed next to each other. Any set of pieces that uniquely determine a triangle will also determine a parallelogram.