Question

step
statement\treason
d is the midpoint of \\(\overline{ac}\\)
\\(\overline{ae} \cong \overline{cf}\\)
\\(\overline{ab} \perp \overline{de}\\)
\\(\overline{bc} \perp \overline{df}\\)\tgiven
2\t\\(\angle aed\\) is a right angle\tselect a reason...

Explanation:

Step1: Recall the definition of perpendicular lines

Perpendicular lines intersect at right angles (90 - degree angles). So if two lines are perpendicular, the angle between them is a right angle.

Step2: Apply the definition to the given lines

We are given that \(\overline{AB}\perp\overline{DE}\). By the definition of perpendicular lines, the angle formed between \(\overline{AB}\) and \(\overline{DE}\), which is \(\angle AED\) (since \(E\) is the intersection point of \(\overline{AB}\) and \(\overline{DE}\) in the diagram), must be a right angle. So the reason for \(\angle AED\) being a right angle is "Definition of Perpendicular Lines" (or "If two lines are perpendicular, then they form right angles").

Answer:

The reason is "Definition of Perpendicular Lines" (or "If two lines are perpendicular, then they form right angles").