SOLUTION: If the diagonals of a parallelogram are perpendicular to each other prove that it is a rhombus

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Question 1121613: If the diagonals of a parallelogram are perpendicular to each other prove that it is a rhombus
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's say it is a parallelogram ABCD
Statements........................................................................................ Reasons
1.Parallelogram AB and CD are perpendicular to each other ......... Given
2. < AMB and < CMB are right angles.............................................. Definition of perpendicular
3. m < AMB+=+90º and m < CMB+=+90º ..............................................Definition of right angle
4. < AMB+ congruent < CMB................................................. ...........Definition of congruent angles
5. AM is congruent MC+........................................................................-Opposite sides of a parallelogram are congruent
6. BM is congruent BM ....................................................................................Reflexive property of congruent
7. ΔAMB is congruent ΔCMB .............................................................. SAS Postulate
8. AB is congruent BC+.......................................................................... CPOCTAC
9. Parallelogram ABCD is a rhombus..........................................Definition of rhombus