Tile
Old English tigele, from Latin tegula, from an Indo-European root meaning ‘cover’.
wiktionary
From Middle English tile, tyle, tigel, tiȝel, teȝele, from Old English tieġle, tiġle, tiġele(“tile; brick”), from Proto-West Germanic *tigulā, from Proto-Germanic *tigulǭ(“tile”), from Latin tēgula. Doublet of tegula.
See tiler(“doorkeeper at a Masonic lodge”).
etymonline
tile (n.)
early 14c., from Old English tigele "roofing shingle," from Proto-Germanic *tegala (Old Saxon tiegla, Old High German ziagal, German ziegel, Dutch tegel, Old Norse tigl), a borrowing from Latin tegula "roof-tile" (source also of Italian tegola, French tuile), from tegere "to roof, to cover," from PIE root *(s)teg- "to cover." Also used in Old English and early Middle English for "brick," before that word came into use.
tile (v.)
"to cover with tiles," late 14c., from tile (n.). Related: Tiled; tiling.