The constitutional provision common in Everson v. Board of Education of the Township of Ewing (1947) and Engel v. Vitale (1962) is "the Establishment Clause of the First Amendment."
The First Amendment's Establishment Clause is used in Everson v. Board of Education of the Township of Ewing (1947) to apply the First Amendment's religion clauses at the state level.
Similarly, in the case of Engel v. Vitale (1962), the same Establishment Clause of the First Amendment was used to rule that the school prayer was unconstitutional.
Hence, in this case, it is concluded that the correct answer is "the Establishment Clause of the First Amendment."
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The constitutional provision common in both Everson v. Board of Education of the Township of Ewing (1947) and Engel v. Vitale (1962) is the First Amendment clause on state sponsorship of religion.
In Engel v. Vitale, the Supreme Court ruled that it was not constitutional for the government to write a prayer for people to recite. However, in Everson v. Board of Education (1947), the Supreme Court ruled that the provision for the transportation of school children in religious schools did not violate the separation of state and religion. It relied upon the Fourteen Amendment to make the judgment.
Thus, in both cases, the common constitutional provision is the First Amendment that forbade government sponsorship of religion.
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