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"Protesta" is a form of "protesta", a noun which is often translated as "protest". "Manifestación" is a noun which is often translated as "demonstration". Learn more about the difference between "protesta" and "manifestación" below.
la protesta(
proh
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tehs
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tah
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (rally)
a. protest 
Se realizó una gran protesta en contra de la guerra frente al Congreso.A massive anti-war protest was staged outside the Congress building.
b. demonstration 
Los estudiantes realizaron una protesta en contra de los recortes en educación.The students organized a demonstration against education cuts.
2. (objection)
a. complaint 
El producto estaba en perfectas condiciones. No entiendo el motivo de tu protesta.The product was in perfect condition. I don't understand the reason for your complaint.
b. protest 
Dije que no quería viajar, pero mis padres ignoraron mi protesta.I said I didn't want to travel, but my parents ignored my protest.
a. promise 
¡No cumplista con tu protesta! Dijiste que me ibas a llamar todos los días.You didn't keep your promise! You said you were going to call me every day.
la manifestación(
mah
-
nee
-
fehs
-
tah
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syohn
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (politics)
a. demonstration 
Estamos organizando una manifestación no violenta mañana en el centro al mediodía.We are organizing a non-violent demonstration downtown tomorrow at noon.
b. protest 
La policía llegó a la manifestación para asegurar que no se volviera violenta.The police arrived at the protest to make sure that it didn't become violent.
2. (indication)
a. display 
La pareja enojó a sus amigos por sus grandes manifestaciones de cariño repetidas en público.The couple annoyed their friends with their constant public displays of affection.
b. sign 
El cambio de color de las hojas es la primera manifestación de que el otoño se aproxima.The change in the color of the leaves is the first sign that fall is coming.
3. (journalism)
a. statement 
Se espera que hoy el jefe de la policía haga una manifestación oficial sobre el escándalo.The police chief is expected to issue an official statement today concerning the scandal.
b. declaration 
Los empleados esperaron pacientemente las manifestaciones que su gerente iba a hacer a la prensa.The employees patiently awaited the declarations that their manager would make to the press.