Question

step\tstatement\treason
\td is the midpoint of \\(\overline{ac}\\)
\t\\(\overline{ae} \cong \overline{cf}\\)
1\t\\(\overline{ab} \perp \overline{de}\\)\tgiven
\t\\(\overline{bc} \perp \overline{df}\\)
2\t\\(\angle aed\\) is a right angle\tperpendicular lines form right angles
3\t\\(\angle cfd\\) is a right angle\tselect a reason...

Explanation:

Step1: Analyze the given perpendicular lines

We know that \( \overline{BC} \perp \overline{DF} \) (from Step 1's statements).

Step2: Apply the perpendicular lines property

The property that perpendicular lines form right angles is a fundamental geometric principle. Since \( \overline{BC} \) and \( \overline{DF} \) are perpendicular, the angle formed between them, \( \angle CFD \), should be a right angle. The reason is the same as for \( \angle AED \): "Perpendicular lines form right angles".

Answer:

Perpendicular lines form right angles