Our friend David Joyce is the expert on all things Euclid. Just looking at his table of contents for Euclid’s Elements we see:

Book I. Propositions (48)
Book II. Propositions (13)
Book III. Propositions (37)
Book IV. Propositions (16)
Book V. Propositions (25)
Book VI. Propositions (37)
Book VII. Propositions (39)
Book VIII. Propositions (27)
Book IX. Propositions (36)
Book X. Propositions ([115])
Book XI. Propositions (39)
Book XII. Propositions (18)
Book XIII. Propositions (18)

48+13+37+16+25+37+39+27+36+115+39+18+18 = 468 theorems in Euclidean geometry, at least as reported by Euclid. A modern reading would probably rule out a fair number of these as not Euclidean Geometry — Book VII is number theory and Book II is geometric descriptions of algebraic identities. In any case there have been quite a few theorems of Euclidean geometry since Euclid, but I don’t know how to count those.