Answer
1. If angle 1 is equal to angle 3 and angle 2 is equal to angle 4, then the sum of angles 1 and 3 (angle AJD) is equal to the sum of angles 2 and 4 (angle JKF).
2. When corresponding angles are congruent, the two lines cut by the bisector are parallel.
3. AJD and JKF are congruent.
4. CD and EF are parallel.
Work Step by Step
1. We first state that AJD and JKF are equal, for we need to show a relationship between the angles formed only by the three lines shown, not by the two rays.
2. We need to show the relation between the angles when the lines are parallel in order to prove that the lines are parallel.
3. We must state that the angles are congruent since we know for the lines to be parallel, the angles must be congruent.
4. Since the angles are congruent, we can conclude that the lines are parallel.
