Question

What is the reason for step 5 in this proof?

A .Vertical Angles Theorem
B. Opposite interior angles of a parallelogram are congruent.
C. All angles of a rectangle have the same measure.
D. Alternate Interior Angles Theorem

Answer 1

Opposite interior angles of a parallelogram are congruent.

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.

Answer 2

B. Opposite interior angles of a parallelogram are congruent.