(01.07 MC) Fill in the missing statement and reason in the proof of the corresponding angles theorem.
D
It is given that AB is parallel to 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.
O CHE and AGF are alternate interior angles; using the Addition Property of Equality
O CHE and AGF are alternate interior angles; using the Subtraction Property of Equality
CHE and AGF are samo-side interior angles; using the Subtraction Property of Equality