Fill in the missing statement and reason in the proof of the Alternate Interior Angles Theorem.
Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.
It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem. ∠EGB and ∠EHD are congruent according to the ________. Finally, ________ by the Transitive Property of Equality.
Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent
Corresponding Angles Theorem; ∠EGB and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠AGF and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent
∠EGB is congruent to ∠EHD by the Alternate Exterior Angles Theorem.
Therefore, by the Transitive Property of Equality, ∠AGF and ∠EHD are congruent.