Sometimes
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Never. A parallelogram has two pairs of equal angles opposite one another. A trapezoid does not.
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It is sometimes true that two parallelograms are similar. The could be congruent, or dissimilar in that one is not an enlargement of the other.
opposite angles of all parallelograms are always equal.
they are not
Yes, Rectangles are always parallelograms
Not always, sometimes two obtuse triangles are similar and sometimes they are not similar.