The veins in their leaves are parallel to each other. Look at the picture of the trillium. The big veins in the leaves are all going in the same direction. Look at the purple crocuses at the top of the page. They also show parallel veins in their petals and long, thin leaves.
Crocuses are also monocotyledons.
The parts of the flowers of monocotyledons are arranged in threes or multiples of threes. Note that the trillium has three petals, and the crocus flowers have six petals. The stamens also follow this pattern. Examples of monocotyledons are the grasses, such as rice, corn, wheat, and sugar cane. The lily family is also a family of monocotyledons.