How do we know Saturday is the Sabbath Day?

Jesus died and was laid in a tomb on Friday, commonly known as “Good Friday”, but known in the Bible as a “preparation day” for the sabbath was about to begin:

Luke 23:52-54 King James Version (KJV)
52 This man went unto Pilate, and begged the body of Jesus.
53 And he took it down, and wrapped it in linen, and laid it in a sepulchre that was hewn in stone, wherein never man before was laid.
54 And that day was the preparation, and the sabbath drew on.

The obvious day in between Friday and Sunday is Saturday, but known as the “sabbath” day in the Bible, according to the 4th Commandment, which the women obeyed and “rested the sabbath day” after Jesus was nailed to the cross and buried:

Luke 23:55-56 King James Version (KJV)
55 And the women also, which came with him from Galilee, followed after, and beheld the sepulchre, and how his body was laid.
56 And they returned, and prepared spices and ointments; and rested the sabbath day according to the commandment.

Jesus rose from the dead on Sunday, commonly known as “Easter Sunday”, but known in the Bible as the “first day of the week”, and the women who prepared the spices did not go to the tomb on Saturday or “sabbath”, but rested on Saturday until Sunday or “the first day of the week” to go to the tomb with the spices:

Luke 24:1-6 King James Version (KJV)
1 Now upon the first day of the week, very early in the morning, they came unto the sepulchre, bringing the spices which they had prepared, and certain others with them.
2 And they found the stone rolled away from the sepulchre.
3 And they entered in, and found not the body of the Lord Jesus.
4 And it came to pass, as they were much perplexed thereabout, behold, two men stood by them in shining garments:
5 And as they were afraid, and bowed down their faces to the earth, they said unto them, Why seek ye the living among the dead?
6 He is not here, but is risen: remember how he spake unto you when he was yet in Galilee,