Name the property that justifies this statement: If AB = BA, then segment AB is congruent to segment BA.


A )Addition Property of Equality
B) Reflexive Property of Congruence
C) Symmetric Property of Congruence
D) Transitive Property of Congruence

Symmetric

Im stuck here too sorry

Symmetric Property

It follows from Definition of Congruent Line Segments where line segments are congruent if they have the same measure or length.

Someone might also say reflexive property of congruence because measure of line segment AB and line segment BA are always equal because they are the same line segments.

The property that justifies the given statement is the Reflexive Property of Congruence, which states that any segment is congruent to itself. In this case, the statement "AB = BA" means that segment AB is equal to segment BA, and since the Reflexive Property states that a segment is congruent to itself, we can conclude that segment AB is congruent to segment BA.

To find the correct property, we need to understand the meanings of each option:

A) The Addition Property of Equality is used when performing operations on both sides of an equation to maintain equality. It is not relevant to this question.

B) The Reflexive Property of Congruence states that any geometric figure (such as a segment, angle, or triangle) is congruent to itself. This property is applicable here, as segment AB is congruent to itself (AB = AB).

C) The Symmetric Property of Congruence states that if segment AB is congruent to segment CD, then segment CD is also congruent to segment AB. This property is not relevant to this question because it involves comparing different segments.

D) The Transitive Property of Congruence states that if segment AB is congruent to segment CD, and segment CD is congruent to segment EF, then segment AB is congruent to segment EF. This property also is not applicable in this case as it involves comparing multiple segments.

Therefore, the correct answer is B) Reflexive Property of Congruence.