Since 1 and 2 are congruent and formed by AD and BC respectively, and are in alternate interior positions, AD and BC are parallel ny the alternate interior angle theorem. AED and DEC equal 180 and so do DEC and CEB, so DEC equals CEB. this means triangle ADE is similar to triangle BEC by AA, so this means angle ADE equals angle CBE. then similar to angles 1 and 2 DC and AB are parallel. then by definition of a parallelogram, the figure is a parallelogram. since it is made of two pairs of parallel line segments
