"هٰذا الْكَلْب تَعْبان اَلْحَمْدُ لِله."
Translation:This dog is tired, praise be to God.
In the Arabic, we have "al" but in the English, it is not used. Shouldn't the sentence be this is "the" tired dog praise be to God?
No. So the way this works is that generally a phrase will agree in definiteness, but a sentence will disagree. So "the big dog" is al-kalb al-kabīr (definite definite), "a big dog" is kalb kabīr (indefinite indefinite), and "the dog is big" is al-kalb kabīr (definite indefinite).
When we start adding in the demonstratives (eg "this"), things get more complicated. Hâdhā and hâdhihi can be thought of as being definite, so hâdhā kalb is "this is a dog". In order to say "this dog" you need it to agree in definiteness: hâdhā al-kalb. If you want to say this is the dog, you actually have to add in a pronoun: hâdhā huwa al-kalb (literally "this it/he the dog").