Is given that overline AB is parallel to overline CD and points E, G, t H and Fare collinear. The measure of angle EGF is 180by the definition of a straight angle. Angle AGE and angle AGF are adjacent, so the measure of angle AGE plus the measure of angle AGF equals the measure of angle EGF , by the Angle Addition Postulate. Then substituting for the measure of angle EGF it can be said that the measure of angle AGE plus the measure of angle AGF equals 180 so the measure of angle CHE plus the measure of angle AG equals 180° Substituting once again means that the measure of angle AGE plus the measure of angle AGF equals the measure of angle CHE plus the measure angle AGF The measure of angle AGE is equal to the measure of angle CHE Finally, by the definition of congruence , angle AGE is congruent to angle CHE .