Question

1. choose the correct answer.

which theorem or postulate shows that ∠6 ≅ ∠7?
same - side interior angles theorem
corresponding angles postulate
vertical angles theorem
alternate exterior angles theorem

Explanation:

• Same - Side Interior Angles Theorem: States that if two parallel lines are cut by a transversal, the sum of same - side interior angles is \(180^{\circ}\). \(\angle6\) and \(\angle7\) are not same - side interior angles.
• Corresponding Angles Postulate: States that if two parallel lines are cut by a transversal, corresponding angles are congruent. \(\angle6\) and \(\angle7\) are not corresponding angles.
• Vertical Angles Theorem: States that vertical angles (opposite angles formed by the intersection of two lines) are congruent. \(\angle6\) and \(\angle7\) are vertical angles (formed by the intersection of line \(m\) and line \(t\)).
• Alternate Exterior Angles Theorem: States that if two parallel lines are cut by a transversal, alternate exterior angles are congruent. \(\angle6\) and \(\angle7\) are not alternate exterior angles.

Answer:

Vertical Angles Theorem.