SOLUTION: How do you prove a parallelogram with two consecutive sides congruent to be a rhombus?

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Question 575889: How do you prove a parallelogram with two consecutive sides congruent to be a rhombus?
Answer by solver91311(24713) About Me  (Show Source):
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Let the four vertices be labeled A, B, C, and D. Since the labeling is arbitrary, there is no loss of generality by assuming that AB and BC are the given congruent sides. By definition of a parallelogram, CD has to be congruent to AB, therefore BC is congruent to CD also. Then for the same reason DA is congruent to CD which is congruent to BC which is congruent to AB. All 4 sides congruent = rhombus.

John

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