That girl studies algebra.
The verb “studies” is transitive, because its meaning is completed by the object “algebra.”
Transitive verbs have voice
From A New English Grammar for Schools, by Thomas Harvey:
I. Voice is an attribute of a transitive verb.
a. Voice shows whether the subject acts, as
The hunter killed a bear,
b. OR is acted upon:
The bear was killed by a hunter.
II. Transitive verbs have two voices.
a. Active voice
The active voice represents the subject as acting upon an object.
John struck a match.
The boy was studying a lesson.
The cat caught the mouse.
The boy was studying a lesson.
The cat caught the mouse.
b. Passive voice
1. The passive voice represents the subject as being acted upon. The direct object of a verb in the active voice becomes its subject in the passive.
The match was struck by John.
The lesson was studied. (by him)
The mouse was caught. (by the cat)
The lesson was studied. (by him)
The mouse was caught. (by the cat)
2. The passive voice is formed by putting some form of the verb to be in front of a transitive verb.
The boy shut the door. (active)
The door was shut by the boy. (passive)
He saw the comet. (active)The comet was seen by him. (passive)
c. Certain verbs are sometimes used with passive meaning in the active voice.
This stick splits easily.
(i.e. The girl split the stick easily.)
Butter sells for forty cents.
(i.e. The merchant sells butter for forty cents.)
This ground plows well.
(i.e. This ground is easy for me to plow.)
The stone breaks readily.
(i.e. The stone is easy for the mason to break.)
d. A few verbs sometimes assume the passive form, but are used in an active sense.
The melancholy days are come.
(i.e. have come)
Babylon is fallen.
(i.e. has fallen.)
She is gone.
(i.e. has gone.)
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