Question

match the statement to the property it shows.
if ab = cd, then cd = ab.
if mn = xy, and xy = ab, then mn = ab.
segment cd is congruent to segment cd.
transitive property
symmetric property
reflexive property

Explanation:

• Reflexive property: A quantity is equal to itself. So, segment \(CD\) is congruent to segment \(CD\) (since congruence of segments is based on equality of lengths and \(CD = CD\))
• Transitive property: If \(a=b\) and \(b = c\), then \(a=c\). Here, if \(MN=XY\) and \(XY = AB\), then \(MN=AB\)
• Symmetric property: If \(a = b\), then \(b=a\). If \(AB=CD\), then \(CD = AB\)

Answer:

• Segment \(CD\) is congruent to segment \(CD\): reflexive property
• If \(MN = XY\), and \(XY=AB\), then \(MN = AB\): transitive property
• If \(AB = CD\), then \(CD=AB\): symmetric property