Option D:
Converse of the corresponding angle postulate
Solution:
1. Given a || b.
2. Alternate Interior angle theorem:
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
⇒ ∠1 ≅ ∠3
3. Given ∠2 ≅ ∠3
4. Transitive property of equality:
If a = b and b = c, then a = c.
So, from (2) and (3), we can say ∠1 ≅ ∠2.
5. ∠1 and ∠2 are corresponding angles.
Converse of the corresponding angle postulate:
If two lines are cut by a transversal and the corresponding angles are equal then the two lines are parallel.
⇒ c || d.
Option D is the correct answer.
Converse of the corresponding angle postulate.