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 \(\overline{GE}\) and another \(\overline{DF}\)
3) Consider these pair of parallel segments:
\(\overline{GD}\parallel \overline{EF}\\\overline{DE}\parallel\overline{GF}\)
4) Now let's examine the angles. According to Euclides since DE and GF are parallels we can say that:
\(\angle \alpha \cong \angle \gamma \\\ \angle \beta \cong \angle \delta\)
5) This step is the conclusion of the previous one, since alternate interior angles have the same measure, so
\(\angle \alpha +\angle \beta \cong \angle \gamma +\angle \delta\)
Opposite interior angles of a parallelogram are congruent.
