step statement reason 1 abcd is a rhombus $\overline{df}$ bisects $\overline{bc}$ given 2 $\overline{be} \cong \overline{ce}$ a segment bisector divides a segment into two congruent segments 3 $\angle dec \cong \angle feb$ vertical angles are congruent 4 $\overline{dc} \parallel \overline{ab}$ opposite sides of a parallelogram / rhombus / rectangle / square are parallel 5 $\angle c \cong \angle ebf$ parallel lines cut by a transversal form congruent alternate interior angles 6 $\triangle dec \cong \triangle feb$ asa 7 $\overline{bf} \cong \overline{dc}$ corresponding parts of congruent triangles are congruent (cpctc) 8 $\overline{dc} \cong \overline{ad}$ image of a rhombus with labeled points d, c, e, b, a and segments

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Accepted Answer

To determine the reason for $\overline{DC}\cong\overline{AD}$ in step 8, we use the properties of a rhombus.

### Step 1: Recall the definition of a rhombus
A rhombus is a parallelogram with all four sides congruent. This means that in rhombus $ABCD$, all sides $AB$, $BC$, $CD$ (or $DC$), and $DA$ (or $AD$) are congruent.

### Step 2: Apply the property to $\overline{DC}$ and $\overline{AD}$
Since $ABCD$ is a rhombus (given in step 1), by the definition of a rhombus, all sides are congruent. Thus, $\overline{DC}\cong\overline{AD}$ because **all sides of a rhombus are congruent**.

# Brief Explanations:
In a rhombus, all four sides are congruent. Since $ABCD$ is a rhombus (given), $\overline{DC}$ and $\overline{AD}$ are sides of the rhombus, so they must be congruent.
# Answer:
All sides of a rhombus are congruent

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QUESTION IMAGE

Question

Explanation:

Step 1: Recall the definition of a rhombus

Step 2: Apply the property to \(\overline{DC}\) and \(\overline{AD}\)

Answer: