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a rhombus is always sometimes or never a parallelogram
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GPT-5 mini
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Always.
Reason: Let ABCD be a rhombus, so AB = BC = CD = DA. Consider diagonal AC. In triangles ABC and ADC we have AB = DC, BC = AD and AC common, so the triangles are congruent (SSS). Hence ∠BAC = ∠DCA, so line AB is parallel to CD; similarly ∠BCA = ∠DAC, so BC is parallel to AD. Both pairs of opposite sides are parallel, so ABCD is a parallelogram.
(If you use the alternate definition "a rhombus is a parallelogram with all sides equal," the conclusion is immediate.)
Reason: Let ABCD be a rhombus, so AB = BC = CD = DA. Consider diagonal AC. In triangles ABC and ADC we have AB = DC, BC = AD and AC common, so the triangles are congruent (SSS). Hence ∠BAC = ∠DCA, so line AB is parallel to CD; similarly ∠BCA = ∠DAC, so BC is parallel to AD. Both pairs of opposite sides are parallel, so ABCD is a parallelogram.
(If you use the alternate definition "a rhombus is a parallelogram with all sides equal," the conclusion is immediate.)
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