Question

quadrilateral wykg is shown.
given: \\( \overline { w g } \cong \overline { k y } \\), \\( \overline { y w } \cong \overline { g k } \\)
prove: \\( \triangle k g w \cong \triangle w y k \\)
an incomplete two - column proof is shown.
\

$$\begin{tabular}{|c|c|c|}hline 1. \\( \\overline { w g } \\cong \\overline { k y } \\), \\( \\overline { y w } \\cong \\overline { g k } \\) & 2. \\( \\overline { w k } \\cong \\overline { w k } \\) & 3. \\( \\triangle k g w \\cong \\triangle w y k \\) \\\\ hline 1. given & 2. & 3. sss congruence \\\\ hline \\end{tabular}$$

what reason can be used to justify the statement in step 2?
reflexive property of congruence
transitive property of congruence
substitution property of congruence
given

Explanation:

Step1: Recall the Reflexive Property of Congruence

The Reflexive Property of Congruence states that any segment is congruent to itself. That is, for a segment \(AB\), \(AB\cong AB\).

Step2: Apply the property to segment \(WK\)

In the statement \(WK\cong WK\), we are dealing with a single segment being congruent to itself. This directly follows the Reflexive Property of Congruence.

Answer:

Reflexive Property of Congruence