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) AD ? CB
(b) ?AEC ? ?BED
(c) ?AEC ? ?AEB
(d) ?CEA ? ?BEA
(a) True for rhombi, but not for non-rhombi parallelograms. Diagonals are perpendicular in a rhombus.
(b) True for both parallelograms and rhombi; vertical angles.
(c) False (supplementary, not congruent)
(d) True for rhombi, but not for non-rhombi parallelograms. Diagonals bisect the opposite angles in a rhombus.
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