Historically, the Church has declared that Mary is worshiped (I.e given the worship of Hyperdulia) so henceforth is it logical to say that we Worship Mary & the Saints (by giving them the worship of Dulia & Hyperdulia) while giving God the (worship of Latria)?
Latria comes from the Greek noun/verb pair λατρεία/λατρεύω, specifically meaning worship rendered to a deity. This is how it is used in the Septuagint and the New Testament. For example, in Deuteronomy 6:13 of the LXX,
κύριον (Lord) τὸν (the) θεόν (God) σου (of you) φοβηθήσῃ (you shall fear) καὶ (and) αὐτῷ (to him) λατρεύσεις (you will adore) καὶ (and) πρὸς (to) αὐτὸν (him) κολληθήσῃ (you shall cleave to) καὶ (and) τῷ (to the) ὀνόματι (name) αὐτοῦ (of him) ὀμῇ (you shall swear).
Essentially, it’s best to translate λατρεύω as “adore” because that’s the kind of worship you’d only give to a deity or figure you believe to contain some kind of divinity. God alone is to be adored and no other.
Worship, in traditional theology, is a broad a term. Worship may be and is given to the Mary and the angels and saints and icons and statues and God and Christ and anything worthy of respect or veneration, this is called dulia (in the case of Mary, hyperdulia). This comes from the Greek noun/verb pair δοῦλος/δουλεύω which signifies serving or being a slave in a general sense. Of course, even though the Latin theological term Dulia already derives from the Greek, I think the meaning of it is better reflected in the Greek verb προσκυνέω. This term can be used broadly, ranging from the kind of worship given to God in latria, to the simple service or respect shown to priests or angels or cultic objects. This is how it is used in the Septuagint. For example, in Daniel 2:46 the LXX has,
τότε (then) Ναβουχοδονοσορ (Nebuchadnezzar) ὁ (the) βασιλεὺς (king) πεσὼν (falling) ἐπὶ (on) πρόσωπον (face) χαμαὶ (on the ground) προσεκύνησε (worshiped) τῷ (to the) Δανιηλ (Daniel)
The Second Council of Nicaea (A.D. 787) allows προσκυνέιν to be given to images but λατρεία to God alone.
It should be noted though that outside of the Greek Bible, προσκυνέιν can be used in a secular way outside of worship which is religious. Yet the translators of the Septuagint and authors of the New Testament appropriated it primarily for religious purposes.
There’s one final qualification I’d like to make. It is discussed by St. John of Damascus as well as St. Thomas Aquinas. This is the notion of relative Latria, that is, the kind of worship given to icons or statues of God or Christ or the cross. Adoration may be afforded here, not to the nature of the depictions or the materials that they are made of, but to what they depict. Our adoration does not pass into the materials, rather it passes onto the divine nature itself which is what is undergoing depiction here. For if we were only to give the depiction of the divine nature mere dulia, then we would only be affording dulia to God when he is worthy of infinitely more.