En geometría, mi profesora me enseñó a trazar un círculo perfecto con el compás.

In this sentence, geometría refers to the school subject or field in a general way, so Spanish often leaves out the article.

• En geometría = in geometry / in geometry class
• En la geometría would sound more like in the geometry of something, or it would need a more specific context.

So here en geometría is the natural choice.

In Spain, profesor/profesora is very commonly used for a teacher, not only a university professor.

• mi profesora = my female teacher
• mi profesor = my male teacher

Also notice that mi does not change for gender:

• mi profesora
• mi profesor

Only the noun changes.

Me means to me here. It is an object pronoun showing who received the teaching.

So:

• mi profesora enseñó = my teacher taught
• mi profesora me enseñó = my teacher taught me

In Spanish, object pronouns like me, te, lo, la, nos usually go before the conjugated verb, so me enseñó is the normal order.

After enseñar when you mean teach someone to do something, Spanish normally uses:

• enseñar a + infinitive

So:

• me enseñó a trazar = she taught me to draw/trace
• me enseñó a leer = she taught me to read
• me enseñó a cocinar = she taught me to cook

Without the a, it would sound ungrammatical in standard Spanish in this structure.

Enseñó is the preterite, which presents the action as a completed event.

Here it suggests something like:

• my teacher taught me on a particular occasion, or
• she taught me and that action is viewed as complete

If you said enseñaba, that would sound more ongoing, habitual, or descriptive:

• mi profesora me enseñaba... = my teacher used to teach me... / was teaching me...

So enseñó fits a finished act of teaching.

Trazar means something like to trace, to draw out, or to construct a line or shape, often in a precise or technical way.

In geometry, trazar is very common because it sounds more exact and methodical than dibujar.

• dibujar un círculo = to draw a circle
• trazar un círculo = to trace/construct a circle, especially with a tool

So in a geometry context, trazar is the more natural verb.

In Spanish, adjectives usually come after the noun, especially when they are simply describing a quality in a neutral way.

• un círculo perfecto = the normal, straightforward way to say a perfect circle

If you say un perfecto círculo, it sounds more literary, emphatic, or stylistically marked. It is not the usual phrasing in an ordinary geometry sentence.

So post-noun adjective placement is the standard choice here.

Yes, compás has more than one meaning. Its meaning depends on context.

Here, because the sentence is about geometry and drawing a circle, el compás means the drawing instrument used to make circles: a compass.

Other meanings exist too, such as:

• compás in music = rhythm / measure
• in some contexts, compás can also suggest compass in the navigation sense, though brújula is the more usual word for that

So in this sentence, compás definitely means the geometry tool.

Using el here is very natural because it refers to the instrument as the standard tool for the task.

• con el compás = with the compass, meaning the compass used for that kind of work
• con un compás would also be possible, but it sounds more like with a compass / with some compass

Spanish often uses the definite article when talking about familiar tools, body parts, clothing, and other things understood from context.

So con el compás sounds more idiomatic here.

En geometría is placed at the beginning as a topic or setting phrase: it tells you the context first.

The comma helps separate that introductory phrase from the main clause:

• En geometría, mi profesora...

In English, this is similar to writing:

• In geometry, my teacher taught me...

The comma is natural because the speaker is first setting the scene, then giving the main information.

The accent marks show where the stress falls and sometimes help distinguish forms.

• enseñó is stressed on the last syllable: en-se-ñó
  • This is the he/she taught form in the preterite.
• círculo is stressed on the first syllable: cír-cu-lo

The written accents are important because they tell you both pronunciation and, in some cases, grammar.

For example:

• enseño = I teach
• enseñó = he/she taught

So the accent is not optional; it changes the form.