All members of this family in our area are easily recognized by the presence of a stipular sheath, or ocrea, which surrounds the stem above the attachment of each leaf. The similar reduced structure in the inflorescence is called an ocreola. The leaves are alternate and the nodes usually enlarged.

1. Achenes winged on the angles, becoming much longer than the perianth (ca. 3-5 times as long); stamens 9; stigmas conspicuous; knobby, subsessile and crowded at the summit of the ovary; leaves palmately veined; stout perennial cultivated for its edible petioles and rarely escaped.

Rheum

1. Achenes not winged (though the perianth may be), no more than twice as long as the perianth (or longer in the annual Fagopyrum); stamens 8 or fewer; stigmas various (feathery, minute, and/or on distinct styles); leaves and habit various.

2. Tepals 6, greenish or reddish, scarcely petaloid, the 3 inner (but not the outer) ones enlarging in fruit and concealing the achene; stigmas a feathery tuft; plants in some species dioecious or polygamous and hence some flowers entirely staminate.

Rumex

2. Tepals 4-5, white to red and ± petaloid at least along the margins, uniform in size or the outer ones larger; stigmas usually not feathery and plants mostly with bisexual flowers.

3. Pedicels with a swollen joint near the middle (but not far above the sheathing ocreolae), solitary in each ocreola, the inflorescence thus composed of slender racemes, appearing jointed because of the overlapping ocreolae; leaves not over 1 (-1.1) mm wide; delicate-looking annual.

Polygonum (in part)

3. Pedicels usually jointed near the summit (if at all), often crowded, the inflorescence various; leaves at least (1.5-) 2 mm wide; annual or perennial, not delicate.

4. Stem and petioles with retrorse prickles; leaves hastate or sagittate (with acute basal lobes).

Persicaria (in part)

4. Stem and petioles without prickles; leaves various.

5. Outer tepals winged or keeled in fruit, or plant somewhat twining or vine-like, or both; leaves ovate-cordate to broadly sagittate.

Fallopia

5. Outer tepals not winged or keeled; plant not twining; leaves various.

6. Leaf blades about as broad as long, ± triangular-cordate; ripe achene 3-sided and much exceeding the perianth; styles 3, small but slender, several times as long as thick; smooth branching annual with the uppermost inflorescences crowded in a ± corymbiform panicle.

Fagopyrum

6. Leaf blades usually much longer than wide, not cordate; achene 2- or 3-sided, included in the perianth or slightly exserted; styles 1-3, in most species scarcely if at all longer than thick (elongate in Bistorta vivipara and Persicaria virginiana); habit various, with flowers in axillary clusters, spikes or dense spike-like inflorescences.

7. Flowers 1-4 at a node, sessile or pediceled in the axils of foliage leaves or bracts; leaf blades jointed at the base, less than 2 (-2.4) cm broad; summit of ocrea silvery white, becoming lacerate-shredded; annuals.

Polygonum (in part)

7. Flowers (or bulblets in Bistorta vivipara) numerous in peduncled terminal or axillary spikes, racemes, or panicles, often densely crowded; leaves not jointed at base of blade, in some species over 2.5 cm broad; summit of ocrea tinged with brown, shattering at maturity but not shredding; annuals or perennials.

8. Leaves mostly basal, rapidly reduced in size up the stem and not more than 3 stem leaves present; many flowers in the single spike converted to bulblets; stems simple.

Bistorta

8. Leaves cauline, more than 3, basal leaves absent; flowers in the often several to many spikes not converted to bulblets; stems usually branched, rarely simple in depauperate individuals.

Persicaria (in part)