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If by four parallel lines you mean two pairs of parallel lines, then you would be looking for a parallelogram. An example of a parallelogram is at this address:
http://upload.wikimedia.org/wikipedia/commons/4/41/Parallelogram.svg
The arrowhead lines along the sides designate that the opposite sides are parallel and of the same length. The single and double lines in each section show that the portions of line in each segment are identically sized.
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Draw a quadrangle that has 2 pairs of parallel sides and no right angles?
Draw a parallelagram this has the opposite sides parallel and no right angles
Draw a quadrangle that has 2 pairs of parallel sides and two right angles?
The figure, as described, is impossible. If a quadrangle has 2 pairs of parallel sides then the number of right angles can be 0 or 4, but not 2.
How many parallel lines does a right angle have?
A right angle has no parallel lines, but it does have perpendicular lines that meet at right angles.
What does quadrangle that has 2 pairs of parallel side and no right angles look like?
A rhombus for example
What lines are not perpendicular?
Parallel lines or lines that don't intersect at right angles
