document.write( "Question 563454: a) Prove the diagonals of a cyclic quadrilateral bisect each other
\n" ); document.write( "b) prove if the diagonals of a quadrilateral bisect each other then the quadrilateral is cyclic.\r
\n" ); document.write( "\n" ); document.write( "I know the opposite sides of the quadrilateral are equal and the SAS theorem proves the triangles made by the diagonals are equal I just dont know how to write the proofs \n" ); document.write( "

Algebra.Com's Answer #364901 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
Statements a) and b) cannot be true, since it is possible to find counterexamples for each one. Note that a cyclic quadrilateral is a quadrilateral whose four vertices all lie on a circle.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For statement a), a \"kite\" shape formed by taking a right triangle and reflecting it about the hypotenuse is a counterexample, since such a quadrilateral is cyclic and not every kite shape will have diagonals that bisect each other.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For statement b), a parallelogram (other than a rectangle) is a counterexample, because its diagonals bisect each other, but parallelograms (other than rectangles) *cannot* be cyclic (since opposite angles must add to 180). \n" ); document.write( "

\n" );