Question

1. choose the correct answer. which theorem or postulate shows that ∠4 ≅ ∠5? alternate interior angles theorem vertical angles theorem same - side exterior angles theorem alternate exterior angles theorem

Explanation:

Step1: Recall the definitions of angle - related theorems

• Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.
• Vertical Angles Theorem: Vertical angles (opposite angles formed by the intersection of two lines) are congruent.
• Same - Side Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the same - side exterior angles are supplementary (sum to \(180^{\circ}\)).
• Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

Step2: Analyze the position of \(\angle4\) and \(\angle5\)

• \(\angle4\) and \(\angle5\) are non - adjacent interior angles that lie on opposite sides of the transversal \(t\). Lines \(l\) and \(m\) are parallel (assumed from the context of angle - relationship theorems for parallel lines).

Answer:

Alternate Interior Angles Theorem