Die brilpoot is aan die brilraam geheg.

Because Afrikaans uses die as the definite article for all genders and for both singular and plural nouns in most ordinary cases.

So here:

• die brilpoot = the glasses arm / temple
• die brilraam = the glasses frame

Unlike English, Afrikaans does not change the article for masculine, feminine, or neuter nouns.

Brilpoot is a compound noun.

It is made from:

• bril = glasses
• poot = leg

Afrikaans, like Dutch and German, very often combines nouns into one word. So brilpoot literally looks like glasses-leg, but it refers to the arm/side piece/temple of a pair of glasses.

This is also a compound noun:

• bril = glasses
• raam = frame

So brilraam means the frame of the glasses.
Again, Afrikaans normally writes this as one word, not as separate words.

Because Afrikaans strongly prefers closed compounds. When two nouns work together to form one idea, they are usually written as one word.

So:

• bril + poot → brilpoot
• bril + raam → brilraam

This is very normal in Afrikaans. English often uses separate words where Afrikaans uses compounds.

Aan is the preposition that goes with geheg in this expression.

So aan ... geheg means attached to.

Even though English uses to, Afrikaans uses aan here. This is something learners usually need to memorize as a set pattern:

• geheg aan = attached to

Geheg is the past participle of the verb heg, which means attach, fasten, or affix.

In this sentence, geheg works like an adjectival participle, describing the state of the object:

• is geheg = is attached

So the sentence is describing a state, not an action happening right now.

Because the sentence is describing the condition of the glasses arm: it is attached.

Compare the ideas:

• heg = to attach / to fasten
• is geheg = is attached

So is + geheg works much like English is attached.
If you used just heg, it would sound like the subject is actively doing the attaching, which is not the idea here.

That is a very common Afrikaans sentence pattern.

The structure here is:

• Die brilpoot = subject
• is = finite verb
• aan die brilraam = prepositional phrase
• geheg = participle/adjectival complement

Afrikaans often places this kind of participle or verbal element toward the end of the clause. So is aan die brilraam geheg is a natural structure.

Yes. That is a very good way to learn it.

It is best to remember:

• geheg aan = attached to

Learning the preposition together with the word will help you sound more natural, because prepositions do not always match English exactly.

Yes, there are other ways to express a similar idea, but aan ... geheg is a neat, correct, slightly formal/technical way to say it.

For example, in more everyday speech, people might sometimes use words related to vas depending on context. But geheg is precise and works well when talking about parts being fixed to each other.

Yes. The finite verb is is present tense.

Even though geheg looks like a past participle, the whole sentence describes a present state:

• the glasses arm is attached now

So this is not a past-tense sentence. It is a present-tense description of a condition.

The plural is usually brilpote.

So you could say:

• Die brilpote is aan die brilraam geheg.

Notice that is stays is, because Afrikaans uses is with both singular and plural subjects in the present tense.

Yes, in this sentence you do, because each noun phrase has its own article:

• die brilpoot
• die brilraam

Each one is a separate definite noun phrase, so each takes die.

It is normal and correct, but it sounds a bit careful or technical, especially because of geheg.

That is not a problem at all. It is exactly the kind of wording you might see in explanations, instructions, descriptions of objects, or more precise writing.