Question

use the given information to prove that f || g. given: ∠2 ≅ ∠6 prove: f || g

Explanation:

Step1: Identify Angle Relationship

$\angle 2$ and $\angle 6$ are corresponding angles (they occupy the same relative position at each intersection where a transversal crosses the two lines \( f \) and \( g \)).

Step2: Apply 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 lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. Since $\angle 2 \cong \angle 6$ (given), by the Converse of the Corresponding Angles Postulate, we can conclude that \( f \parallel g \).

Answer:

To prove \( f \parallel g \) given \( \angle 2 \cong \angle 6 \):

1. Identify the angle relationship: $\angle 2$ and $\angle 6$ are corresponding angles (formed by the transversal intersecting lines \( f \) and \( g \)).
2. Apply the Converse of the Corresponding Angles Postulate: If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. Since $\angle 2 \cong \angle 6$ (given), by this postulate, \( f \parallel g \).

Thus, \( f \parallel g \) is proven using the Converse of the Corresponding Angles Postulate.