=Bistort, Polygonum viviparum.=

29b. Stem branched, submerged in water or creeping on muddy shores
(flowers pink) =Water Smartweed, Polygonum amphibium.=

30a. Raceme single or two; leaves broadly ovate-lanceolate, about 3
times as long as wide =Smartweed, Polygonum muhlenbergii.=

30b. Racemes numerous; leaves lanceolate, 4-6 times as long as wide
--31.

31a. Racemes drooping or nodding at the tip
=Smartweed, Polygonum lapathifolium.=

31b. Racemes erect =Smartweed, Polygonum pennsylvanicum.=

32a. Leaves arrow-shape, the basal lobes pointing backward
=Tear-thumb, Polygonum sagittatum.=

32b. Leaves halberd-shape, the basal lobes pointing sidewise
=Tear-thumb, Polygonum arifolium.=

33a. The three outer sepals becoming conspicuously winged in fruit
(False Buckwheat) --34.

33b. The sepals all unchanged in fruit, except in size (Black Bindweed)
--35.

34a. Wings of the fruit with wavy-curled margins
=False Buckwheat, Polygonum scandens.=

34b. Wings of the fruit flat
=False Buckwheat, Polygonum dumetorum.=

35a. Leaf-sheaths with a ring of bristles at the base
=Black Bindweed, Polygonum cilinode.=

35b. Leaf-sheaths without a ring of bristles
=Black Bindweed, Polygonum convolvulus.=

CHENOPODIACEAE, the Goosefoot Family

Herbs, with inconspicuous greenish or reddish flowers without petals, in
summer.

1a. Leaves linear or nearly so, entire --2.

1b. Leaves of a broader shape, usually toothed or lobed --5.

2a. Leaves rather stiff, narrowly linear or thread-like, with
spine-like tips
=Russian Thistle, Salsola kali var. tenuifolia.=

2b. Leaves soft, not spine-like --3.

3a. Widely branched, rather diffuse, 1-5 dm. tall; plant of the shore of
the Great Lakes =Bug-seed, Corispermum hyssopifolium.=

3b. Erect plants with ascending branches --4.

4a. Leaves glabrous (3-6 dm. tall)
=Goosefoot, Chenopodium leptophyllum.=

4b. Leaves minutely ciliate on the margin (bushy branched, 5-10 dm.
tall) =Kochia, K