Answer:
Opposite interior angles of a parallelogram are congruent.
Step-by-step explanation:
To answer this question let's do it step by step. So step
1) Consider the parallelogram GDEF
2) Trace a straight line, since two points define a line. Trace [tex]\overline{GE}[/tex] and another [tex]\overline{DF}[/tex]
3) Consider these pair of parallel segments:
[tex]\overline{GD}\parallel \overline{EF}\\\overline{DE}\parallel\overline{GF}[/tex]
4) Now let's examine the angles. According to Euclides since DE and GF are parallels we can say that:
[tex]\angle \alpha \cong \angle \gamma \\\ \angle \beta \cong \angle \delta[/tex]
5) This step is the conclusion of the previous one, since alternate interior angles have the same measure, so
[tex]\angle \alpha +\angle \beta \cong \angle \gamma +\angle \delta[/tex]
Opposite interior angles of a parallelogram are congruent.
