What is the property of congruence that justifies the following statment If WT ¯¯¯¯¯¯¯¯¯¯ ≅ XY ¯¯¯¯¯¯¯¯¯ then XY ¯¯¯¯¯¯¯¯¯ ≅ WT¯¯¯¯¯¯¯¯¯
The property of congruence that justifies the statement is the Symmetric Property of Congruence. According to this property, if two segments (or any other geometric figures) are congruent, then their order can be reversed without changing the congruence. Therefore, if WT is congruent to XY, it follows that XY is congruent to WT.
The property of congruence that justifies the statement "If WT is congruent to XY, then XY is congruent to WT" is the Symmetric Property of Congruence.
According to the Symmetric Property of Congruence, if two line segments are congruent, then their corresponding sides are also congruent. In other words, if segment A is congruent to segment B, then segment B is congruent to segment A.
Applying this property, if WT is congruent to XY, then XY is also congruent to WT. This is because the order of the line segments does not affect their congruence.
The property of congruence that justifies the statement "If $\overline{WT} \cong \overline{XY}$, then $\overline{XY} \cong \overline{WT}$" is the Symmetric Property of Congruence.
The Symmetric Property of Congruence states that if two segments or angles are congruent, then their order can be reversed. In other words, if $\overline{AB} \cong \overline{CD}$, then $\overline{CD} \cong \overline{AB}$.
To explain how to justify this statement using the property, we can say the following:
1. Given: $\overline{WT} \cong \overline{XY}$ (Given information)
2. By the Symmetric Property of Congruence, if two segments are congruent, their order can be reversed.
3. Applying the Symmetric Property, we can conclude that $\overline{XY} \cong \overline{WT}$.
Thus, the Symmetric Property of Congruence justifies the statement "If $\overline{WT} \cong \overline{XY}$, then $\overline{XY} \cong \overline{WT}$".