Final answer:
The Sixth Amendment is common to both Gideon v. Wainwright and Betts v. Brady, ensuring the right to counsel for those who cannot afford an attorney in criminal trials.
Step-by-step explanation:
The constitutional amendment common to both Gideon v. Wainwright and Betts v. Brady is the Sixth Amendment. This amendment guarantees the rights of criminal defendants, including the right to a public trial without unnecessary delay, the right to a lawyer, the right to an impartial jury, and the right to know who your accusers are and the nature of the charges and evidence against you.
In Gideon v. Wainwright, the Supreme Court ruled that the Sixth Amendment requires the states to provide defense attorneys to criminal defendants charged with serious offenses who cannot afford lawyers themselves. This landmark case expanded the rights initially affirmed in Betts v. Brady, which held that the state must provide a public defender in certain special circumstances. However, Gideon v. Wainwright overruled Betts v. Brady to some extent by establishing that state courts are required under the Sixth Amendment to provide counsel in criminal cases for defendants unable to afford their own attorneys, without the special circumstances test established in Betts v. Brady.