Question 55418
Prove: A parallelogram is a rhombus if and only if its diagonal bisect the oppostie angles.
1..ABCD IS A PARALLELOGRAM(P.G.) AND AC IS ANGLE BISECTOR OF ANGLES A AND C.... AND BD IS ANGLE BISECTORS OF ANGLES B AND D
T.S.T.ABCD IS A RHOMBUS
ANGLE DAB = ANGLE DCB .OPPOSITE ANGLES IN A P.G.ARE EQUAL
AC BISECTS ANGLES DAB AND DCB...GIVEN
HENCE IN TRIANGLE ABC 
ANGLE CAB = ANGLE DAB/2 = ANGLE DCB/2=ANGLE ACB
HENCE ABC IS ISOCELLES TRIANGLE
HENCE AB=BC .SIDES OPPOSITE EQUAL ANGLES
BUT AB=CD   AND BC=AD....OPPOSITE SIDES OF P.G. ARE EQUAL
HENCE AB=BC=CD=DA
HENCE ABCD IS RHOMBUS
2.ABCD IS A RHOMBUS ..T.P.T DIAGONALS BISECT OPPOSITE ANGLES.
WRITE THE PROOF IN REVERSE MANNER TO THAT GIVEN ABOVE 
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