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"La tablilla" is a form of "tablilla", a noun which is often translated as "splint". "La varilla" is a form of "varilla", a noun which is often translated as "rod". Learn more about the difference between "la tablilla" and "la varilla" below.
la tablilla(
tah
-
blee
-
yah
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (medicine)
a. splint 
Tengo que usar una tablilla en el brazo porque me lastimé jugando al baloncesto.I have to wear a splint on my arm because I hurt myself playing basketball.
2. (culinary) (Central America) (Mexico)
Regionalism used in Central America: Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica, and Panama
Regionalism used in Mexico
a. tablet 
Ve al quiosco y compra dos tablillas de chocolate para el mole.Go to the store and buy two tablets of chocolate for the mole sauce.
a. notice board 
La notificación en la tablilla dice que el fin de semana que viene van a fumigar el edificio.The notification on the notice board says the building will be fumigated next weekend.
la varilla(
bah
-
ree
-
yah
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
a. rod 
Una larga varilla de acero mantiene al maniquí de pie.A long steel rod supports the mannequin.
b. bar 
Las varillas de la jaula están casi pegadas, así que el loro no puede escaparse.The bars of the cage are closely spaced and the parrot cannot escape.
c. spoke  (of a bicycle wheel or an umbrella)
Las varillas de la rueda delantera están torcidas.The spokes of the front wheel are twisted.
d. rib  (of an umbrella or a fan)
El fuerte viento dobló mi paraguas y rompió las varillas.The strong wind turned my umbrella inside out and broke its ribs.
e. earpiece  (on a pair of glasses)
Las varillas de mis gafas son de plástico.The earpieces of my glasses are made of plastic.
f. arm  (on a pair of glasses)
Las varillas de mis lentes de sol son muy frágiles.The arms of my sunglasses are very fragile.
2. (clothing)
a. stay 
Las varillas del corsé me aprietan, y no puedo respirar bien.The stays in my corset are too tight and I can't breathe properly.
3. (colloquial) (anatomy)
A word or phrase that is commonly used in conversational speech (e.g., skinny, grandma).
a. jawbone 
El boxeador de rojo recibió un gancho que le quebró la varilla.The boxer in red trunks took an uppercut that broke his jawbone.
4. (colloquial) (trifle) (Mexico)
A word or phrase that is commonly used in conversational speech (e.g., skinny, grandma).
Regionalism used in Mexico
a. cheap wares 
No desperdicies tu dinero en esa varilla.Don't waste your money on those cheap wares.
b. trinkets 
Los vendedores callejeros venden comida y varilla.The street vendors sell food and trinkets.
5. (annoyance) (Caribbean)
Regionalism used in the Caribbean: Cuba, the Dominican Republic, and Puerto Rico