The Greek word for righteousness is …. “ dikaiosyne “ which is the LORD God always acts in righteousness .

Righteousness and justice are the foundation of your throne;
love and faithfulness go before you… Psalm 89: 14
but let him who boasts boast about this:
that he understands and knows me,
that I am the LORD, who exercises kindness,
justice and righteousness on earth,
for in these I delight,"
declares the LORD…… Jer. 9:24

That is He always has a right relationship with people and His action is to maintain that relationship .

As God acts in righteousness ( because HE IS righteous ) so He called Israel to be righteous as His chosen people . They were placed in a covenant in right relationship with Him through faith and were expected to live in right relationship with others .

Abraham was an example of a righteous man . Abraham was in a ‘ right relationship” with God .

Gen 21:1-7 And not only that but he trusted God completely and fully .

How many of us would have put their only son on an alter to kill him as a sacrifice as God had asked ?

Abrahams faith in God is a genuine example to us . Righteousness is revealed from faith - For in the gospel a righteousness from God is revealed, a righteousness that is by faith from first to last just as it is written: "The righteous will live by faith ….. Romans 1:17

Righteousness is through our faith in God .
Righteousness means a right relationship with both God and one's fellow human beings .

Matt 5:6.... Blessed are those who hunger and thirst for righteousness,
for they will be filled.

20...... For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.
The hebrew word is sadig and means a right relationship with both God and and others and the scriptures that I have in post 2 are from the N. T. and others are Luke 18:14.... I tell you that this man, rather than the other, went home justified before God. For everyone who exalts himself will be humbled, and he who humbles himself will be exalted."

The gospel is effective because along with the proclamation , a righteousness goes forth .

Romans 1: 16-17....I am not ashamed of the gospel, because it is the power of God for the salvation of everyone who believes: first for the Jew, then for the Gentile.
17For in the gospel a righteousness from God is revealed, a righteousness that is by faith from first to last, just as it is written: "The righteous will live by faith."
Jesus has made us righteous with His righteousness.

Psalm 4:1
Hear me when I call, O God of my righteousness: thou hast enlarged me when I was in distress; have mercy upon me, and hear my prayer.

1 Corinthians 1:30 But it is from Him that you have your life in Christ Jesus, Whom God made our Wisdom from God, [revealed to us a knowledge of the divine plan of salvation previously hidden, manifesting itself as] our Righteousness [thus making us upright and putting us in right standing with God], and our Consecration [making us pure and holy], and our Redemption [providing our ransom from eternal penalty for sin].
1 Peter 2:24

He himself bore our sins in his body on the tree, so that we might die to sins and live for righteousness; by his wounds you have been healed.

2 Corinthians 5:20-21

We are therefore Christ's ambassadors, as though God were making his appeal through us. We implore you on Christ's behalf: Be reconciled to God.

21God made him who had no sin to be sin for us, so that in him we might become the righteousness of God.

What does it mean to become the righteousness of God ? ...Because we are called to be ambassadors for Christ , we are representatives of Christ while here on earth and as we do this we gain access to true righteousness .