Name the Property of Congruence that justifies the following statement: If XY = WX , then WX = XY. Reflexive Property of Congruence Transitive Property of Congruence Distributive Property of Congruence Symmetric Property of Congruence
Symmetric Property of Congruence
The property of congruence that justifies the statement "If XY = WX, then WX = XY" is the symmetric property of congruence.
The property that justifies the statement "If XY = WX, then WX = XY" is the Symmetric Property of Congruence.
To understand why, let's break down each property:
1. Reflexive Property of Congruence: This property states that any geometric shape is congruent to itself. For example, if XY is a line segment, then XY is congruent to XY. However, this property does not apply to the given statement because it's not relating an entity to itself.
2. Transitive Property of Congruence: This property states that if two objects are congruent to a third object, then they are congruent to each other. For example, if A is congruent to B, and B is congruent to C, then A is congruent to C. However, this property does not apply to the given statement because it does not involve three distinct objects.
3. Distributive Property of Congruence: The distributive property is a property of arithmetic operations, not congruence. Therefore, it does not apply to the given statement.
4. Symmetric Property of Congruence: This property states that if two geometric figures are congruent, then they can be reversed or flipped to show that the same relationship holds. For example, if XY is congruent to WX, then WX is congruent to XY. This property applies to the statement because it involves two line segments (XY and WX) that are stated as congruent, and it affirms that the order of the segments does not affect the congruence relationship.
In summary, the Symmetric Property of Congruence is the property that justifies the statement "If XY = WX, then WX = XY."