Incongruous means inappropriate or out of place, something which is not consistent or harmonious.
Incongruous is an adjective.
Synonyms: unsuitable, conflicting, incompatible, contradictory.
Antonyms: suitable, congruous, appropriate, consistent, consonant, fitting, harmonious.
At the beginning the two concepts appeared to be incongruous, but they are actually quite compatible.
Your incongruous statements make me question the veracity of your story.
The room was decorated with an incongruous mixture of modern and old furnishings.