That would not be correct in British English. The past participle is "shown" or (rarely seen now) "shewn". See http://www.verbix.com/webverbix/English/show.html
"I showed her my house" would be okay.
The article you cite doesn't seem to deal with the point. The only mention of the participle is of "shewed" as an obsolete form (and I am not sure that is correct anyway).
Yes, of course it is "laten zien"! But English speakers have no knowledge of this ..., or, in Dutch: Maar daar hebben Engelstaligen geen kaas van gegeten...
The course developers should have included this phrase elsewhere in the course; in the exercise with verb forms in various tenses, the translation with two verbs in the infinitive one after the other ["laten zien"] is a problem.