1	Fruiting pedicels recurved or rarely spreading; pistillate sepals mostly erect and closely enclosing flower or fruiting head, occasionally spreading to recurved.		(2)
+	Fruiting pedicels spreading to ascending or absent; pistillate sepals mostly spreading to recurved, not enclosing flower.		(9)
2 (1)	Leaves, at least some, emersed.		(3)
+	Leaves submersed, floating, rarely emersed, or plants stranded on shore.		(5)
3 (2)	Fruiting heads 1.2--2.1 cm diam.; leaf blade hastate to sagittate		3 Sagittaria montevidensis
+	Fruiting heads 0.7--1.2 cm diam.; leaf blade linear-ovate to lance-elliptic.		(4)
4 (3)	Achenes abaxially keeled, mostly more than 2 mm; faces not tuberculate, often with glands; California .		5 Sagittaria sanfordii
+	Achenes not abaxially keeled, mostly less than 2 mm, faces tuberculate, without glands; e of Rocky Mountains.		6 Sagittaria platyphylla
5 (2)	Achene faces tuberculate; floating leaves with sagittate blades present at least on some plants of population.		2 Sagittaria guayanensis
+	Achene faces not tuberculate; floating leaves absent or, if present, with unlobed or hastate blades.		(6)
6 (5)	Fruiting pedicels 0.2--1.1 cm; phyllodia lenticular in cross section; tidal muds; mostly brackish waters.		1 Sagittaria subulata
+	Fruiting pedicels 1.5--6.5 cm; phyllodia flattened in cross section; rarely tidal muds; mostly fresh waters.		(7)
7 (6)	Leaves with blades and petioles usually present on some plants; some plants often stranded along shore, these usually with expanded leaf blades.		7 Sagittaria filiformis
+	Leaves all phyllodia; plants almost always submersed, rarely stranded, these without expanded leaf blades.		(8)
8 (7)	Phyllodia 50--250 cm; Florida springs.		8 Sagittaria kurziana
+	Phyllodia 12--53 cm; streams and lakes, New Mexico.		4 Sagittaria demersa
9 (1)	Filaments pubescent to tomentulose (except S. fasciculata).		(10)
+	Filaments glabrous.		(17)
10 (9)	Leaves all phyllodia, nearly terete; ne United States.		9 Sagittaria teres
+	Leaves with blades and petioles or if phyllodia, then flattened to triangular in cross section; mostly widespread.		(11)
11 (10)	Pistillate flowers sessile to subsessile .		16 Sagittaria rigida
+	Pistillate flowers obviously pedicellate.		(12)
12 (11)	Filaments cylindric .		14 Sagittaria lancifolia
+	Filaments dilated.		(13)
13 (12)	Rhizomes present, coarse; stolons and corms absent.		(14)
+	Rhizomes absent or if present, then not coarse; corms and/or stolons present.		(15)
14 (13)	Abaxial wing of fruit ± entire; plants widespread		13 Sagittaria graminea
+	Abaxial wing of fruit scalloped or toothed; ne Alabama		12 Sagittaria secundifolia
15 (13)	Filaments exceeding anthers in length.		17 Sagittaria cristata
+	Filaments shorter than or equaling anthers in length.		(16)
16 (15)	Blades of emersed leaves 0.5 cm or more wide; w Carolinas.		11 Sagittaria fasciculata
+	Blades of emersed leaves, if present, 0.4(--0.5) cm or less wide; se coastal plain.		10 Sagittaria isoetiformis
17 (9)	Emersed leaf blades linear to ovate.		(18)
+	Emersed leaf blades cordate, sagittate, or hastate.		(20)
18 (17)	Bracts papillose.		15 Sagittaria papillosa
+	Bracts not papillose.		(19)
19 (18)	Emersed plants with erect to ascending petioles; leaf blades lanceolate to ovate.		18 Sagittaria ambigua
+	Emersed plants with recurved petioles; leaf blades linear to sagittate.		19 Sagittaria cuneata
20 (17)	Bracts distinct or connate much less than ¼ total length.		(21)
+	Bracts connate at least ¼ total length.		(23)
21 (20)	Flowers in 2--4 whorls; achenes with facial glands.		20 Sagittaria engelmanniana
+	Flowers in 5--12 whorls; achenes without facial glands.		(22)
22 (21)	Petiole winged in cross section; achene beak strongly recurved.		21 Sagittaria australis
+	Petiole ridged in cross section; achene beak ascending apically.		22 Sagittaria brevirostra
23 (20)	Achene beak 1--2 mm, horizontal.		24 Sagittaria latifolia
+	Achene beak 0.1--0.6 mm, erect or incurved.		(24)
24 (23)	Emersed plants with recurved petioles and linear to sagittate blades; basal lobes equal to or shorter than remainder of blade; submersed leaves phyllodial, floating leaves cordate to sagittate		19 Sagittaria cuneata
+	Emersed plants with ascending to erect petioles and sagittate blades; basal lobes longer than remainder of blade; submersed and floating leaves absent.		23 Sagittaria longiloba