Are lances and nets and versatile weapons considered one-handed weapons?

Question

The Bladesinging Wizard gets the Training in War and Song feature, which states (SCAG, p. 142; emphasis mine):

[...] You gain proficiency with one type of one-handed melee weapon of your choice [...]

Similarly, there is the Dual Wielder feat, which states (PHB, p. 165; emphasis mine):

[...] You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one [...]

Could a Wizard then choose the lance or Versatile weapon to gain proficiency in? (They can't choose the net because it's ranged.)

Could somebody with Dual Wielder draw/stow a lance, net, or Versatile weapon? None of them have the Two-Handed property, but they do have either the Special or Versatile properties so I'm unsure how this works out. Do nets and lances and Versatile weapons count as one-handed weapons?

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The following question already exists but it only establishes that a lance while mounted counts as a one-handed weapon:

• Can you dual wield lances?

Answer 1

The rules implicitly assume that non-two-handed weapons are one-handed

The two-handed property says:

This weapon requires two hands when you attack with it.

For weapons without the two-handed property, I can't find anything in the rules that directly says they are considered one-handed. However, although there is no explicit "one-handed" weapon property, there is strong circumstantial evidence that the designers consider all non-two-handed weapons to be one-handed weapons. First, the Crossbow Expert feat and the ammunition property both which make explicit reference to "one-handed weapons". In addition, the rules for melee attacks say:

A melee attack typically uses a handheld weapon such as a sword, a warhammer, or an axe.

Similarly, the rules for improvised weapons also reference holding the weapon in your hands:

An improvised weapon includes any object you can wield in one or two hands, such as broken glass, a table leg, a frying pan, a wagon wheel, or a dead goblin.

And assuming that all PCs have 2 hands (which is currently the case for all official playable races), the only ways to wield a handheld weapon are with either 1 hand or 2.

Finally, a few official rulings in the Sage Advice Compendium also reference one-handed weapons, such as:

Dual Wielder

Can my character wield two heavy weapons if she has the Dual Wielder feat? No. The Dual Wielder feat lets you wield two one-handed weapons. Every heavy weapon in the Player’s Handbook also has the two-handed property.

This ruling strongly implies that any non-two-handed weapon is considered a one-handed weapon, or else it wouldn't be eligible for two-weapon fighting. In general, although it's never explicitly stated, the intent seems to be that every weapon either requires 1 or 2 hands to wield, so any handheld weapon that isn't two-handed must be one-handed.

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(This answer was adapted from my answer to another question.)

Answer 2

Weapons are two-handed if they have the two-handed property.

A weapon that does not have the two-handed property is one-handed.

The lance does not have the two-handed property, so it is not a two-handed weapon. It just has a special rule that requires you to wield it two handed:

Lance 10 gp 1d12 piercing 6 lb. Reach, special

...

Also, a lance requires two hands to wield when you aren't mounted.

Net doesn't have the two-handed property either:

Net 1 gp - 3 lb. Special, thrown (range 5/15)

Versatile weapons are not two-handed either, they just gain special damage when wielded with two hands:

This weapon can be used with one or two hands. A damage value in parentheses appears with the property--the damage when the weapon is used with two hands to make a melee attack.

If you wield a weapon with two hands and it does not have this property, then it deals normal damage. For example when wielding a dagger with two hands it deals 1d4 damage still.