5. Parallel Lines and Parallelograms

Figure 10	If two lines, are cut by a transversal, the lines are parallel if and only if the alternate interior angles are equal. See Figure 10.
Figure 11	A parallelogram is a quadrilateral whose opposite sides are parallel. It is a theorem that the quadrilateral ABCD is a parallelogram if and only if and have equal magnitudes and directions, that is, if and only if See Figure 11.