Question

What is the reason for step 5 in this proof?

Answer 1

B. Opposite interior angles of a parallelogram are congruent.

Answer 2

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.