(15 points) fill in the missing statement and reason in the proof of the corresponding angles theorem.

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.