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) F (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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