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Is a quadrilateral a parallelogram if 2 pairs of opposite sides are congruent and one pair of opposite angles congruent?

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2 Answers

Not necessarily. In a parallelogram, if you construct a diagonal you will create two congruent triangles. But in the given quadrilateral, if you construct a diagonal opposite to both of the equal angles, you create two triangles that only have SSA congruency; so the two triangles are not congruent and the quadrilateral is not a parallelogram.
Wups; I read it wrong. I read it as though "pair of" wasn't there. Michael is right.
OTOH, the language might be interpreted as a kite.
It seems to me that the equality of the angles is a distraction.  If you attach 4 rods together where the first and the third are equal as are the second and fourth, you can't construct a quadrilateral which isn't a parallelogram.  Think of the rods as having hinges on each end.  The triangles constructed in Steve's answer have sss congruency.  The diagonal, no matter which, is common to both triangles.


Thank you Steve.  The question really needs to be clearer.  Kite is really neat.