Given that ∠2 ≅ ∠6.

Which theorem proves that line d is parallel to line e.
Alternate interior angle theorem

Converse of the alternate interior angle theorem

Alternate Exterior angle theorem

Converse of the alternate exterior angle theorem

The theorem that proves that lines d and e are parallel to each other, given that <2 is congruent to <6 is: D. Converse of the alternate exterior angle theorem

When a transversal cuts across two parallel lines, there are special angles formed having relationship with each other.

For two lines to be parallel, such relationship must exist. That is what a converse theorem seeks to prove.

We are told that <2 is congruent to <6.

Both angles are exterior angles that also lie opposite each other along the transversal. That makes them alternate exterior angles.

<2 will be congruent to <6 if lines d and le are parallel to each other.

Therefore, the theorem that proves that lines d and e are parallel to each other, given that <2 is congruent to <6 is: D. Converse of the alternate exterior angle theorem

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Given that ∠2 ≅ ∠6. Which theorem proves that line d is parallel to line e. Alternate interior angle theorem Converse of the alternate interior angle theorem Alternate Exterior angle theorem Converse of the alternate exterior angle theorem

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Given that ∠2 ≅ ∠6.

Which theorem proves that line d is parallel to line e.
Alternate interior angle theorem

Converse of the alternate interior angle theorem

Alternate Exterior angle theorem

Converse of the alternate exterior angle theorem