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

I need help with this.

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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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.

Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
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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.