SOLUTION: Write a proof argument for part (b) of the sufficient conditions for a parallelogram theorem: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilater

Question 81613This question is from textbook Geometry
: Write a proof argument for part (b) of the sufficient conditions for a parallelogram theorem: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
given: that the opposite sides are congruent.
prove: that the figure ABCD is a parallelogram
I drew in diagonals in the figure ABCD and labeled the point where they intersect E.
please help me solve this proof and provide the justifactions
this is very important. PLEASE try to get this back to me by the end of May 10th
thank you very much This question is from textbook Geometry

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you can prove that the 2 triangles formed by drawing the diagonal are congruent by SSS ... you are given that the opposite sides are congruent and the diagonal is congruent to itself

using the congruency of the two triangles, you can prove that the alternate angles at the ends of the diagonal are congruent (corresponding parts of congruent triangles are congruent) ... this proves the parallelism of the opposite sides by equal alternate interior angles
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