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 he did not actually believe what they did was good. Alternate translation: "If you treated Jerub Baal and his family with honesty and sincerity"

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. Alternate translation: "his family" (See: rc://en/ta/man/translate/figs-metonymy)