
fröhlich
cheerful
Being in a cheerful and carefree mood; expressing joy and good spirits.
Die Kinder sangen ein fröhliches Lied.
The children sang a cheerful song.
cheerful
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cheerful
Being in a cheerful and carefree mood; expressing joy and good spirits.
Die Kinder sangen ein fröhliches Lied.
The children sang a cheerful song.

merry
Describing a festive and joyful atmosphere, often used in fixed expressions and greetings for holidays.
Ich wünsche dir fröhliche Weihnachten und ein gutes neues Jahr!
I wish you a Merry Christmas and a Happy New Year!
'Fröhlich' (cheerful) belongs to the word family of 'froh' (glad) and 'die Freude' (joy). All of these words express a feeling of happiness and good spirits.
Er hat ein sehr fröhliches Wesen und lacht oft.
He has a very cheerful nature and laughs often.
'Fröhlich' (cheerful/cheerfully) can also be used as an adverb to describe how an action is performed. It then remains unchanged after the verb.
Die Vögel zwitscherten fröhlich am Morgen.
The birds chirped cheerfully in the morning.
In its general meaning, 'fröhlich' (cheerful) often describes a mood or atmosphere. Common combinations are 'eine fröhliche Stimmung' (a cheerful atmosphere), 'ein fröhliches Lachen' (a cheerful laugh), or 'fröhliche Musik' (cheerful music).
Auf der Party herrschte eine fröhliche Stimmung.
There was a cheerful atmosphere at the party.
In the second meaning, 'fröhlich' (merry) occurs almost only in fixed holiday greetings. The best known are 'Fröhliche Weihnachten!' (Merry Christmas!) and 'Fröhliche Ostern!' (Happy Easter!).
Wir wünschen allen unseren Freunden fröhliche Ostern!
We wish all our friends a happy Easter!
happy / lucky
Both words can describe a positive mood. „Fröhlich“ refers especially to visible cheerfulness and a good mood, while „glücklich“ expresses a personal, sometimes deeper feeling of well-being. „Fröhlich“ fits observable behavior, while „glücklich“ is more suitable for an inner state.

Auf dem Fest lachte sie viel und wirkte fröhlich.
She laughed a lot at the party and seemed cheerful.
Sie sagt, dass sie mit ihrem neuen Leben glücklich ist.
She says that she is happy with her new life.