هذه بطاقة المكتبة.

Because بطاقة is a feminine singular noun, and the demonstrative must match it.

• هذا = this for masculine singular
• هذه = this for feminine singular

Since بطاقة means card and is feminine, you say:

هذه بطاقة المكتبة

not هذا بطاقة المكتبة.

A useful clue is that بطاقة ends in ة (taa marbuuTa), which very often marks a feminine noun.

In Modern Standard Arabic, هذه is usually pronounced haadhihi.

A rough breakdown is:

• ها = haa
• ذِ = dhi
• هِ = hi

So: haa-dhi-hi

In careful MSA, that final hi is there. In everyday speech, many dialects pronounce this word differently, but for MSA haadhihi is the standard form.

In Arabic, the verb to be in the present tense is usually not written or spoken in simple sentences like this.

So Arabic says literally:

هذه بطاقة المكتبة
This the-library card

But in natural English, we translate it as:

This is the library card.

This kind of sentence is called a nominal sentence in Arabic. The present-tense is/am/are is understood automatically.

Because بطاقة المكتبة is an iDaafa construction, often called a possessive or genitive construction.

In an iDaafa:

• the first noun does not take الـ
• the second noun can make the whole phrase definite

So:

• بطاقة = card
• المكتبة = the library

Together:

بطاقة المكتبة = the library's card / the library card

Even though بطاقة has no الـ, the whole phrase is definite because المكتبة is definite.

It is an iDaafa phrase: card of the library.

Structure:

• بطاقة = the first noun, the thing being possessed
• المكتبة = the second noun, the possessor

So literally it is:

card of the library

In smoother English, that becomes:

• the library card
• sometimes the library's card, depending on context

This is a very common Arabic pattern.

That is exactly how iDaafa works.

In an iDaafa:

1. the first noun does not take الـ
2. the second noun shows whether the whole phrase is definite or indefinite

Compare:

• بطاقة مكتبة = a library card / card of a library
• بطاقة المكتبة = the library card / card of the library

So the definiteness comes from المكتبة.

No, not if you mean the library card.

In an iDaafa, the first noun should not take الـ. So:

• correct: بطاقة المكتبة
• incorrect for this meaning: البطاقة المكتبة

If you put الـ on both words, it breaks the normal iDaafa structure.

So after هذه, the correct phrase is:

هذه بطاقة المكتبة

In fully inflected MSA, it would be:

هذِهِ بِطاقَةُ الْمَكْتَبَةِ

Here is why:

• بطاقةُ ends in -u because it is the predicate of the sentence and is nominative
• المكتبةِ ends in -i because the second noun in an iDaafa is genitive

So the full case-marked form is:

هذِهِ بِطاقَةُ الْمَكْتَبَةِ

In normal writing for learners and in most everyday printed Arabic, these short vowels are often omitted.

Because the noun is part of an iDaafa construction.

The first noun in an iDaafa:

• does not take الـ
• does not take tanween

So by itself, an indefinite noun might be:

• بطاقةٌ = a card

But in iDaafa, it becomes:

• بطاقةُ المكتبةِ = the library card

So losing tanween is one sign that the noun is in an iDaafa.

Not exactly. هذه is a demonstrative, not an adjective.

It points to something: this.

The basic structure is:

• هذه = this
• بطاقة المكتبة = the library card

So the sentence is essentially:

This [is] the library card.

It is not the same as a noun followed by an adjective, like:

• بطاقة كبيرة = a big card

Here, هذه is functioning as the demonstrative subject of the sentence.

Usually no. Because بطاقة المكتبة is a definite phrase, it normally means:

the library card
or
the card of the library

If you wanted This is a library card, you would normally say something like:

هذه بطاقة مكتبة

without الـ on مكتبة.

So the الـ in المكتبة matters a lot.

مكتبة usually means library or sometimes bookstore, depending on context.

It comes from the root ك-ت-ب, which is related to writing and books. Other words from the same root include:

• كتاب = book
• كتب = he wrote
• كاتب = writer
• مكتب = office / desk

So مكتبة is a place connected with books or writing.

هذه بطاقة المكتبة is the normal way to say:

This is the library card.

If you say:

بطاقة المكتبة هذه

that usually means:

this library card

So the difference is:

• هذه بطاقة المكتبة = This is the library card.
• بطاقة المكتبة هذه = this library card

Both are possible patterns, but they do not mean exactly the same thing.

Three things are especially useful:

1. Match the gender

   • هذه goes with feminine بطاقة

2. Recognize the iDaafa

   • بطاقة المكتبة is one connected phrase: the library card

3. Don't try to say an Arabic word for present-tense is

   • just read it directly as:
   • haadhihi biTaaqatu al-maktabati in full formal pronunciation
   • or without case endings in pause: haadhihi biTaaqat al-maktaba

That will make the sentence sound much more natural.