SOLUTION: Prove that if in a cyclic quadrilateral, one pair of opposite angles is congruent, then the other pair of opposite sides is parallel

Algebra ->  Geometry-proofs -> SOLUTION: Prove that if in a cyclic quadrilateral, one pair of opposite angles is congruent, then the other pair of opposite sides is parallel      Log On


   

Question 568387: Prove that if in a cyclic quadrilateral, one pair of opposite angles is congruent, then the other pair of opposite sides is parallel
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I don't think that statement is true. If one pair of opposite angles in a cyclic quadrilateral is congruent, then both angles must be 90 (since opposite angles in a cyclic quadrilateral add up to 180, 180/2 = 90). It is definitely possible to construct a cyclic quadrilateral satisfying that property without any parallel sides.



Not completely drawn well, but you get the picture. If angles A and C are congruent in cyclic quadrilateral ABCD, then A and C are right angles. There are no parallel sides.