To show that ABDE is a parallelogram, we need to prove that opposite sides are parallel. Since side ED is produced to form ABCE, we can see that angle AED and angle CDE are corresponding angles and are therefore congruent.
Similarly, angle ADE and angle CED are alternate interior angles and are congruent as well.
Since corresponding angles and alternate interior angles are congruent, we can conclude that opposite sides AB and DE are parallel.
To show that ABCE is a trapezium, we need to prove that at least one pair of opposite sides is parallel. We have already shown that AB and DE are parallel.
Lastly, to show that AB = EC, we can use the fact that ED = DC = 3 cm. Since DE and DC are congruent, and opposite sides of a parallelogram are congruent, we can conclude that AB = EC.
In summary:
(1) ABDE is a parallelogram because opposite sides AB and DE are parallel.
(2) ABCE is a trapezium because one pair of opposite sides, AB and DE, are parallel.
(3) AB = EC because opposite sides of a parallelogram are congruent, and DE = DC.