en_tn/jdg/09/19.md

If you acted with honesty and integrity with Jerub Baal and his house

Jotham offered the possibility that what they did was good, but Jotham does not actually believe what they did was good. AT: "If you treated Jerub Baal and his family as they deserved to be treated" (See: rc://en/ta/man/translate/figs-hypo)

Jerub Baal

This is another name for Gideon. It means "let Baal defend himself." See how you translated this in Judges 6:32.

his house

Here "house" refers to family. AT: "his family" (See: rc://en/ta/man/translate/figs-metonymy)