Righteousness is the condition of abounding in right thoughts and actions. The technical definition is the easy part. To decide what is admirable, in this case, righteous, is the hard part.
The ancient Jews used the (transliterated) word Tzedaqah to represent the concept of rightneousness. A person who practiced Tzedaqah was said to abound in the condition of being in accordance with all that was right and proper. That said, the Jews then spent centuries defining and redefining what it meant to be in accordance with the right and proper, so that they might abound in that condition.
By the period of the Late Second Temple/Early Rabbis, the Jewish word/concept Tzedaqah had so been identified with almsgiving it meant almost nothing else. This development is unfortunate for later religionists because it would seem to make giving money the sum total of rightneousness. We are attached to our money, to be sure, but lamely offering trifles of cash without explanantion of the "right thought" behind the act cheats the student, the giver and the recipient.
Tzedeqah was the constant fulfilment of all legal and moral obligations by consistent practice of right acts from a right motive. Therefore, righteousness was actually a constant pursuit of justice and a constant practice of good deeds. Good deeds would ultimately bring the world to a utopian condition, as men perfected themselves and their world. Then, Messiah would come because the world would be worthy of Messiah.
In the Late Second Temple culture, discipline to live a righteous life was defined as a learned (practiced) trait for the sustained performance of positive deeds. The disciplined deeds marked a man as righteous, their absence meant he was wicked. A righteous man was said to be alive even after death, while a wicked man was said to be dead even when he was alive.
So, righteousness was not just believing in something or someone as a rational act, as the Greeks would make it later. The Jewish Jesus would have learned the Jewish definition of Tzedaqah. He would have consistently practiced it, as a good Jew.
If we want to love and follow Jesus, we must love Him as He presented Himself. That is, He presented Himself as a Man, as a Jew and as the Savior. He could be one Man among Men, a Jew among Jews but He must stand alone as Savior becaue of the Cross and the Resurrection.
A Righteous person must become so out of pure thought and positive actions. He must practice Teshuva. This is repentance but less developed than the Greek word for repentance, metanoia. Teshuva means a change of direction in terms of action and thought but for the sake of doing good deeds, out of which one might be transformed. Christians would do well to see how metanoia adds the condition of a grace-changed soul but we should be careful not to think this is just a single legal act declaring us righteous without changed actions and thoughts.
Teshuva altered actions in relation to pure, kind living. The Jews who hang out bags of bread on the streets for the poor to eat practice Teshuva to Tzedaqah.
Tzedaqah as almsgiving recognizes the right of the poor to eat and the obligation of the affluent to feed them. The affluent bread-giver actually marked himself as righteous (alive, a Messiah bringer) when he gave to the needy. He must hold back nothing in his heart (seat of intellect) but give without thought of return. He must limit his giving only to what would not hinder the moral and spiritual progress of the poor.
In so doing, the affluent (who need not be super wealthy to give, but only able) had to see the right of the poor to have bread and the blessing the giver received by giving. The Jews in Jesus' crowds (almost all His hearers in Scripture) did not have to strain to understand what Jesus meant when He said "it is more blessed to give than receive," as Paul reports.
Then, it becomes the responsibility of the newly affluent, the poor who have received, to give to someone who does not have bread. If the poor get only to consume they do not practice Teshuva and so die in their wickedness, for they do not seek Tzedaqah.
Naturally, Christians of the Covenant believe grace (Xaris) saves but we cannot ignore the ancient Jewish teaching Jesus would have heard as a boy. Jesus spent His ministry teaching among people who would have believed in Teshuva and Tzedaqah. He added His own perfect body and blood to the human search for personal salvation. Messiah has come. The presence of Messiah obligates/enables Christians to consistently seek justice and practice morality.
This is righteousness that saves aboundingly as it lifts the heart of the affluent out of pride and the heart of the needy out of selfish consumption. Founded in grace, beleived by faith, practiced in discipline, righteous acts mark a righeous person.
Opinions here are mine alone.