Question 188432
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ABCD is a parallelogram.  Given.


AD congruent to AB.  Given.


AD = AB.  Definition of congruence


AB congruent to DC and AD congruent to BC.  Definition of a parallelogram.


AB = DC and AD = BC. Definition of congruence.


If AB = AD and AB = DC, then AB = DC.  Reflexive property of equality


If AD = AB and AD = BC, then AB = BC.  Reflexive property of equality


In summary, AB = AD = DC = BC.  Hence, ABCD is a parallelogram with 4 equal sides.


Therefore, ABCD is a rhombus.  Definition of a rhombus.


QED.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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