Hi Kate
I don't know if it is a house plant, the leaves look like a type of willowherb. Epilobium maybe?
Look at the photos of Epilobium ciliatum, the leaf venation matches well.
http://www.kuleuven-kulak.be/b...
E. hirsutum has a similar growth habit but the leaves are more hairy.
When it flowers can you post the photos? I might be way off track but flowers should help.
