It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. The measure of ∠EGF is 180°, by the definition of a straight angle. ∠AGE and ∠AGF are adjacent, so the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠EGF, by the Angle Addition Postulate. Then, substituting for the measure of ∠EGF it can be said that the measure of ∠AGE plus the measure of ∠AGF equals 180°. , so the measure of ∠CHE plus the measure of ∠AGF equals 180°. Substituting once again means that the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠CHE plus the measure of ∠AGF. The measure of ∠AGE is equal to the measure of ∠CHE . Finally, by the definition of congruence, ∠AGE is congruent to ∠CHE. ∠CHE and ∠AGF are alternate interior angles; using the Addition Property of Equality ∠CHE and ∠AGF are alternate interior angles; using the Subtraction Property of Equality ∠CHE and ∠AGF are same-side interior angles; using the Subtraction Property of Equality ∠CHE and ∠AGF are same-side interior angles; using the Addition Property of Equality