name the property of congruence that justifies the statement:if ab=cd and cd=ef then ab=ef
The property of congruence that justifies the statement "if AB=CD and CD=EF, then AB=EF" is the Transitive Property of Congruence.
The property of congruence that justifies the statement "if ab = cd and cd = ef, then ab = ef" is the Transitive Property of Congruence.
To understand how it applies in this situation, let's break it down:
1. The given statement states "ab = cd" and "cd = ef". These are two separate congruence statements.
2. The Transitive Property of Congruence states that if two quantities are congruent to the same value, then they are congruent to each other.
3. By applying the Transitive Property, we can combine the two congruence statements: "ab = cd" and "cd = ef" to conclude that "ab = ef".
Thus, the Transitive Property of Congruence justifies the statement that "if ab = cd and cd = ef, then ab = ef".