There can never be any parallel lines in a triangle because it has three angles that add up to 180 degrees. This means that the three sides can never not meet. A line that is parallel to another line can never cross it, and the sides of a triangle must always cross each other.
To see if two lines are parallel, connect them with a third line and see if it makes a right angle. When you connect two sides of a triangle with a third line, you can never make a right angle. When this new line is drawn between the sides of a shape with parallel lines, like a parallelogram, it makes a right angle.