Final answer:
The Sixth Amendment—which guarantees fairness in criminal trials and the right to counsel—is common to both Gideon v. Wainwright and Betts v. Brady, with Gideon v. Wainwright establishing the requirement for state courts to provide counsel for those who cannot afford it under this amendment.
Step-by-step explanation:
The constitutional amendment common to both Gideon v. Wainwright and Betts v. Brady is the Sixth Amendment, which ensures fairness in criminal trials. In these landmark cases, the Sixth Amendment's guarantee to the right of assistance of counsel for defendants in criminal trials was at stake. Gideon v. Wainwright expanded on the provisions of Betts v. Brady by ruling that state courts are required under the Sixth Amendment to provide counsel in criminal cases for defendants who are unable to afford their own attorneys, thereby incorporating this aspect of the Sixth Amendment to the states through the Fourteenth Amendment's Due Process Clause.
The Sixth Amendment is a crucial element of the Bill of Rights that maintains the integrity of the judicial process by ensuring a fair and speedy trial, a jury of one's peers, the right to confront witnesses, and the critical right to legal representation. Gideon v. Wainwright underscored the importance of this right and marked a significant turning point in the American legal system, ensuring that all individuals, regardless of their financial means, have access to legal representation in felony trials.