هذه علاقة جيدة.

Because علاقة is a feminine singular noun, and Arabic demonstratives agree with the gender and number of the thing being referred to.

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

So with علاقة, you use هذه.

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

So Arabic says:

• هذه علاقة جيدة
• literally: this good relationship

but the natural English meaning is This is a good relationship.

If you wanted past tense, Arabic would use a verb, for example with كان.

علاقة is grammatically feminine. One strong clue is the ending ة, called tāʾ marbūṭa.

Many Arabic nouns ending in ة are feminine, though not every single one. In this sentence, you should treat علاقة as feminine, and that affects the words that agree with it.

Because adjectives in Arabic must agree with the noun they describe.

Here, جيدة describes علاقة, so it matches it in:

• gender: feminine
• number: singular
• definiteness: indefinite
• case: nominative in full formal grammar

So:

• masculine singular: جيد
• feminine singular: جيدة

Since علاقة is feminine singular, the adjective must be جيدة.

In Arabic, descriptive adjectives normally come after the noun, not before it.

So:

• علاقة جيدة = a good relationship

This is the normal order in Arabic:

• noun + adjective

That is different from English, where we usually say:

• adjective + noun

Because هذه علاقة جيدة and هذه العلاقة الجيدة are different structures.

• هذه علاقة جيدة = This is a good relationship
• هذه العلاقة الجيدة = this good relationship

In هذه علاقة جيدة, هذه stands by itself as this, and علاقة جيدة is the predicate of the sentence.

In هذه العلاقة الجيدة, the demonstrative is directly attached to a definite noun phrase, so both the noun and adjective are definite with ال.

This is a very common and important distinction in Arabic.

Not in the same way as in هذه العلاقة.

In هذه علاقة جيدة, هذه is better understood as a standalone demonstrative meaning this, and علاقة جيدة is what is being said about it.

So the sentence structure is roughly:

• هذه = the subject
• علاقة جيدة = the predicate

That is why the noun after it can be indefinite.

In fully vocalized formal Arabic, you would write:

هذه علاقةٌ جيدةٌ

Why ـٌ on both words?

Because علاقة جيدة is the predicate of a nominal sentence, and the predicate is in the nominative case.

A few notes:

• هذه does not take a normal case ending here
• in everyday writing, these short vowels are usually omitted
• in normal speech, many speakers also do not pronounce the full endings

A careful formal pronunciation is:

hādhihi ʿalāqatun jayyidatun

In pause, many speakers would say something closer to:

hādhihi ʿalāqa jayyida

A useful detail:

• the final ة often sounds like -a in pause
• but when full endings are pronounced, the hidden t appears, as in ʿalāqatun

They mean slightly different things.

• هذه علاقة جيدة = This is a good relationship
• العلاقة جيدة = The relationship is good

So هذه علاقة جيدة introduces or identifies something as a good relationship, while العلاقة جيدة talks about a specific known relationship and says something about it.

This difference comes from the presence of هذه and from whether the noun is indefinite or definite.