Question

use the diagram shown. if ∠1 ≅ ∠2, which conclusion can be made? a. a || b b. o || d c. o ⊥ a d. b ⊥ d

Explanation:

Step1: Recall the Corresponding Angles Postulate

The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is equal. Conversely, if two corresponding angles are equal, then the lines cut by the transversal are parallel.

Step2: Identify the Angles and Lines

In the diagram, \( \angle 1 \) and \( \angle 2 \) are corresponding angles formed by the transversal (either line \( a \) or \( b \)) intersecting lines \( c \) and \( d \). Given that \( \angle 1 \cong \angle 2 \), by the converse of the Corresponding Angles Postulate, the lines \( c \) and \( d \) must be parallel.

Answer:

B. \( c \parallel d \)