a) Corresponding angles theorem; b) vertical angles theorem; c) transitive property
Explanation:
A) ∠2 and ∠6 are on the same side of the transversal and on corresponding sides of their line they are on. This is the definition of corresponding angles, and the corresponding angles theorem tells us they are congruent.
B) ∠4 and ∠2 are opposite angles that share only a vertex. This is the definition of vertical angles, and the vertical angles theorem tells us they are congruent.
C) We know that ∠2≅∠6 and ∠4≅∠2. Using the transitive property, we can then say that ∠2≅∠6.
