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, Kochia scoparia.= 5a. Principal leaves with a broad truncate, rounded, or hastate base --6. 5b. Principal leaves narrowed to the base --12. 6a. Leaves broadly ovate, with 1-4 large sharp projecting teeth on each side =Goosefoot, Chenopodium hybridum.= 6b. Leaves hastate or triangular-ovate, entire or with many teeth --7. 7a. Leaves entire or merely undulate --8. 7b. Leaves sharply or sinuately toothed --9. 8a. Stem erect, simple or sparingly branched =Good King Henry, Chenopodium bonus-henricus.= 8b. Stem diffuse or ascending, freely branched =Orache, Atriplex patula.=