Why can't a triangle have parallel sides?

Answer 1

For two sides to be parallel they must not meet at a point (vertex).

A triangle has only 3 sides.

Let the vertices of a triangle be ABC; then the 3 sides of the triangle are AB, AC and BC.

The sides AB and AC meet at vertex A, so they cannot be parallel.

The sides AB and BC meet at vertex B, so they cannot be parallel.

So Side AB is not parallel to AC (meets at vertex A) and not parallel to BC (meets at vertex B).

The only possibility left is that side BC is parallel to side AC.

But the sides BC and AC meet at vertex C so they cannot be parallel.

Thus none of the sides of a triangle can be parallel.