The predicted geometry of TeF4 by VSEPR theory is trigonal bipyramidal.

Explanation:
VSEPR theory, which stands for Valence Shell Electron Pair Repulsion theory, is a model used to predict the shapes of molecules based on the arrangement of electron pairs around the central atom. According to this theory, the electron pairs around the central atom will arrange themselves in a way that minimizes electron repulsion and maximizes the distance between them.

In the case of TeF4, the central atom is Te (tellurium) and it is surrounded by four fluorine atoms (F). To determine the geometry of the molecule, we first need to determine the number of electron pairs around the central atom.

Tellurium (Te) has six valence electrons, and each fluorine atom (F) contributes one additional valence electron, for a total of 34 valence electrons. The Lewis structure for TeF4 would be:

Te:Valence electrons = 6
F: Valence electrons = 7 (1 from each fluorine atom)

Total valence electrons = 6 + 4(7) = 34

Next, we distribute the electrons around the central atom to minimize electron repulsion. Since there are four bonding pairs of electrons (one from each F atom) and no lone pairs of electrons, the electron pairs will be arranged in a trigonal bipyramidal geometry.

In a trigonal bipyramidal geometry, there are two different types of positions for the electron pairs: equatorial and axial positions. The three equatorial positions lie in a plane and are separated by 120 degrees, while the two axial positions are above and below the plane and are separated by 180 degrees.

Therefore, the predicted geometry of TeF4 according to VSEPR theory is trigonal bipyramidal.