tegan - this is introduced later. As for potato, not 100% sure, but I believe tatws is both the plural and singular form.
I believe 'tatan' or 'taten' is the singular for 'tatws' but.. that may just be a local thing where I'm from
Tatw, tatan or taten is the singular on Anglesey according to my Welsh speaking other half! :-)
How come these Welsh dictionaries spells this word with just one 'n': 'teganau' http://welsh-dictionary.ac.uk/gpc/gpc.html and http://www.geiriadur.net/index.php?page=ateb&term=tegan&direction=we&type=all&whichpart=exact?
Because duolingo is wrong on that and the mistake is not being corrected for some mysterious reason nobody knows.
Is this borrowed from a Germanic language (it sounds a little like English toy, German Zeug /tool/, ...) or is a native Celtic word? At first I thought it may be related to the Irish teach /house/, but apparently the later is cognate with the Welsh tŷ, not tegan.