Question

which lines are parallel if \\( \angle 6 \cong \angle 7 \\)? justify your answer.

1. which lines are parallel if \\( \angle 6 \cong \angle 7 \\)?

a. \\( a \\| b \\); converse of the corresponding angles theorem
b. \\( l \\| m \\); converse of the corresponding angles theorem
\\( a \\| b \\)
converse of the corresponding
angle theorem
\\( l \\| m \\)
converse of the corresponding
angle theorem

Explanation:

Step1: Recall the Corresponding Angles Theorem

The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then the corresponding angles are congruent. The converse of this theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Step2: Identify the lines and transversal

In the given diagram, when we consider \(\angle6\) and \(\angle7\), the transversal is line \(a\) (assuming the standard diagram structure). \(\angle6\) and \(\angle7\) are corresponding angles. If \(\angle6\cong\angle7\), by the converse of the Corresponding Angles Theorem, the lines \(l\) and \(m\) (the two lines that are cut by the transversal \(a\)) are parallel.

Answer:

\(l\parallel m\); Converse of the Corresponding Angle Theorem