Use the parallelogram from Example 1 to verify that the opposite angles in a parallelogram are congruent and consecutive angles are supplementary given that [math]\overline{AD}\parallel\overline{BC}[/math] and [math]\overline{AB}\parallel\overline{DC}[/math].
[list=1] [*]Extend the lines in the parallelogram to show two pairs of intersecting lines and label the angles with numbers. [*]Prove [math]\angle 4 \cong\angle 9[/math]. [*]Prove [math]\angle 7 \cong\angle 14[/math]. [*]Prove that consecutive angles of a parallelogram are supplementary. [/list]