The reasons that completes this two-column proof include the following;
Blank 1 is: 2. Alternate Interior Angles Theorem.
Blank 2 is: 4. Linear Pair Postulate.
Blank 3 is: 5. Substitution Property.
The alternate interior angles theorem states that when two parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
By applying the alternate interior angles theorem to the triangle, we have the following pair of congruent angles;
m∠2 ≅ m∠4
m∠3 ≅ m∠5
In Mathematics and Euclidean Geometry, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both intersect at a point or form a linear pair;
m∠DCB + m∠5 = 180°