
traurig
sad
Feeling or expressing a state of sorrow, suffering, or dejection.
Er war sehr traurig, als er von dem Unglück hörte.
He was very sad when he heard about the accident.
sad
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sad
Feeling or expressing a state of sorrow, suffering, or dejection.
Er war sehr traurig, als er von dem Unglück hörte.
He was very sad when he heard about the accident.

sad
Describing a circumstance or situation that is regrettable or evokes sympathy and sadness.
Das ist eine traurige Geschichte mit einem tragischen Ende.
That is a sad story with a tragic ending.

pitiful
Describing a thing or performance as deplorable, pathetic, or of very poor quality.
Für eine professionelle Mannschaft war das eine ziemlich traurige Vorstellung.
For a professional team, that was a pretty pitiful performance.
The adjective 'traurig' (sad) is closely related to the noun 'die Trauer' (grief, the deep pain over a loss) and the verb 'trauern' (to grieve). All of these words describe the state of sorrow.
Nach dem Tod ihres Hundes war ihre Trauer sehr groß.
After the death of her dog, her grief was very great.
To state the reason for the sadness, the preposition 'über' with the accusative is often used. The construction is: 'traurig sein über etwas' (to be sad about something).
Sie ist traurig über das schlechte Prüfungsergebnis.
She is sad about the poor exam result.
In colloquial language, 'traurig' (sad/pitiful) can also describe very poor quality or performance and then sounds disparaging. Here it means something like 'armselig' (pathetic) or 'erbärmlich' (miserable).
Fünf richtige Antworten von zwanzig sind ein trauriges Ergebnis.
Five correct answers out of twenty is a pitiful result.
It is easy to recognize whether a person has a feeling or a thing triggers a feeling. 'Jemand ist traurig' (someone is sad) describes a person. 'Etwas ist traurig' (something is sad), e.g. a story, describes a thing that makes people sad.
Der kleine Junge ist traurig, weil sein Spielzeug kaputt ist.
The little boy is sad because his toy is broken.
bad
Schlecht directly describes the low quality of a performance. Traurig can disparage the same performance as particularly pitiful or deplorable, making the judgment more subjective and harsher. Schlecht is more suitable for an objective evaluation.

Die Leistung der Mannschaft war heute wirklich traurig.
The team’s performance was really pathetic today.
Die Leistung der Mannschaft war heute schlecht.
The team’s performance was poor today.