Old English tæcan (past tense tæhte, past participle tæht) "to show, point out, declare, demonstrate," also "to give instruction, train, assign, direct; warn; persuade," from Proto-Germanic *taikijan "to show" (source also of Old High German zihan, German zeihen "to accuse," Gothic ga-teihan "to announce"), from PIE root *deik- "to show, point out." Related to Old English tacen, tacn "sign, mark" (see token). Related: Taught; teaching.
Lemonade Vendor (Edgar Kennedy), enraged: I'll teach you to kick me!
Chico: you don't have to teach me, I know how. [kicks him]
The usual sense of Old English tæcan was "show, declare, warn, persuade" (compare German zeigen "to show," from the same root); while the Old English word for "to teach, instruct, guide" was more commonly læran, source of modern learn and lore.
mid-13c., tohte "stretched or pulled tight," possibly from tog-, past participle stem of Old English teon "to pull, drag," from Proto-Germanic *theuhanan, from PIE root *deuk- "to lead," which would connect it to tow (v.) and tie. Related: Tautness.