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 )

Explanation:

• For \(AB = CD\Rightarrow CD = AB\): The symmetric property states that if \(a = b\), then \(b=a\). Here \(a = AB\) and \(b = CD\).
• For \(MN = XY\) and \(XY = AB\Rightarrow MN = AB\): The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\). Here \(a = MN\), \(b = XY\), and \(c = AB\).
• For segment \(CD\cong CD\): The reflexive property states that \(a=a\) (or a segment is congruent to itself). Here \(a\) is segment \(CD\).

Answer:

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