Deuteronomy 2:36 (ESV)

36 From Aroer, which is on the edge of the Valley of the Arnon, and from the city that is in the valley, as far as Gilead, there was not a city too high for us. The LORD our God gave all into our hands.

The battle and Israel's victory went far beyond Jahaz. The city of Aroer marked the southern end of the victory, and Gilead marked the northern limit of the victory. In the whole region that Israel conquered, the Lord gave all towns and cities into their hands.