Question

3 ∠cfd is a right angle perpendicular lines form right angles
4 △aed is a right triangle the triangle contains a right angle
5 △cfd is a right triangle the triangle contains a right angle
6 \\(\overline{ad} \cong \overline{dc}\\) select a reason...
search for reasons...
reflexive property
transitive property
substitution
corresponding parts of congruent triangles are congruent (cpctc)
in a triangle, sides opposite of congruent angles are congruent
a segment bisector divides a segment into two congruent segments
a midpoint divides a segment into two congruent segments
a opposite sides of a parallelogram / rhombus / rectangle / square are congruent
the diagonals of a rectangle / square are congruent
all sides of a rhombus / square are congruent

Explanation:

Step1: Analyze the statement $\overline{AD} \cong \overline{DC}$

We need to find a reason why segment \( AD \) is congruent to segment \( DC \). A midpoint of a segment divides the segment into two congruent segments. If \( D \) is the midpoint of \( AC \), then \( \overline{AD} \cong \overline{DC} \). Among the given options, "A midpoint divides a segment into two congruent segments" fits this situation.

Step2: Select the correct reason

From the list of reasons, the one that explains \( \overline{AD} \cong \overline{DC} \) is "A midpoint divides a segment into two congruent segments".

Answer:

A midpoint divides a segment into two congruent segments