Question

proving lines parallel
use the figure for exercises 1 - 4. using the given information, which lines can you conclude are parallel? state the theorem or postulate that justifies each answer.

1. ∠1≅∠4 alternate exterior angles theorem
2. ∠2≅∠3 corresponding angles theorem
3. ∠6≅∠7
4. m∠5 + m∠8 = 180° consecutive interior angles theorem

Explanation:

Step1: Identify angle - pair relationship for ∠6 and ∠7

∠6 and ∠7 are alternate interior angles.

Step2: Apply relevant theorem

The Alternate Interior Angles Theorem states that if alternate interior angles are congruent, then the lines are parallel.
Since ∠6≅∠7, lines \(d\) and \(e\) are parallel.

Answer:

Lines \(d\) and \(e\) are parallel by the Alternate Interior Angles Theorem.