Determine if each statement is true if
(i) ABCD is a parallelogram
(ii) ABCD is a rhombus
In each case, if true, explain why.
(a) AE = DE
(b) AE = CE
(c) AC = AB
(d) AB = CD
(a) True for both parallelograms and rhombi. Diagonals bisect each other in all
parallelograms
(b) False
(c) True for both parallelograms and rhombi. Opposite sides are congruent in all
parallelograms
(d) True for rhombi, but not for non-rhombi parallelograms. All sides are congruent in a rhombus.
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