Final answer:
The justification for statement 4 in a two-column proof depends on the context of the proof. The corresponding angles theorem, vertical angles theorem, substitution property of equality, and transitive property of equality all apply in different scenarios within geometric proofs.
Step-by-step explanation:
To determine which statement correctly justifies statement 4 of a two-column proof, we need to know the specific context of the statement within the proof. However, without the context of statement 4, we can discuss what each of the provided justifications generally represents within the scope of geometric proofs:
- Corresponding angles theorem is used when two lines are cut by a transversal, and the angles in matching corners are equal.
- Vertical angles theorem states that when two lines intersect, the opposite angles, called vertical angles, are congruent.
- Substitution property of equality allows one to replace one quantity with another equal quantity within an expression or an equation.
- Transitive property of equality suggests that if one quantity equals a second, and the second equals a third, then the first equals the third.
For example, if statement 4 involves showing that two angles are equal because they are both equal to a third angle, the transitive property of equality is the correct choice. If it involves a relationship between angles created by intersecting lines, the vertical angles theorem may be justified. Statement 4 would rely on the corresponding angles theorem if it involves parallel lines cut by a transversal.