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Yes. Draw a triangle without its base line. From both the base vertices draw a line to the opposite side(somewhere in the middle). The four lines so created will meet in 6 points.
It might depend on how you draw it, but I don't think it is possible. Draw the figure, and look at the points where lines meet. Count how many of those points are "odd", meaning that an odd number of lines meets there. Each of these points has to be either the starting point, or the end point, and you can only have one starting point and one end point.
Draw two parallel lines of unequal length, and connect their end points. If you have a right angle, it is a right trapezoid. If the non-parallel sides are equal in length, it is an isosceles trapezoid.
To draw a square with 3 lines, you can draw two perpendicular lines to form a right angle. Then, draw a diagonal line connecting the endpoints of the two perpendicular lines. This diagonal line will complete the square shape with only 3 lines.
2 lines