What is the relationship between "he taught us" and "Tortoise"?
It has to do with the pronunciation of the au and or sounds. The literally English pronunciation (the pronunciation in the English used in England) of the letter r, is not normally rhotic. If you learn of the non-rhotic pronunciation of the sound or and compare it with the English pronunciation of the au sound, you will understand. This makes the sounds of these two sounds, the same.
Therefore, the word taught and the "tort" part of the word tortoise, are pronounced the same. A lot of English (and other British) pronunciation is not rhotic.
There is another point worth making, in relation to this. Even though the word taught and the "tort" part of the word tortoise rhyme, the words "taught us" and "tortoise" do not always rhyme in British English pronunciation.
There are people who pronounce them exactly the same. There are also people who pronounce tortoise as "tor-tos"; with a non-rhotic r and the os sound involving another, common pronunciation of the letter o; as it is in the British pronunciation of the words dog and copper. This, particular pronunciation of the letter o is in the English of England but, not in the English of North America (American English and Canadian English).