Question

Which property justifies the statement: "If Z1 = Z2 and Z2 = Z3, then Z1 = Z3"?

A. Transitive Property of Congruence
B. Commutative Property of Congruence
C. Symmetric Property of Congruence
D. Reflexive Property of Congruence

Answer 1

The property that justifies the statement "If Z1 = Z2 and Z2 = Z3, then Z1 = Z3" is the Transitive Property of Congruence.

Step-by-step explanation:

The property that justifies the statement "If Z1 = Z2 and Z2 = Z3, then Z1 = Z3" is the Transitive Property of Congruence (choice D). This property states that if two things are each congruent to a third thing, then they are congruent to each other. In this case, if Z1 is congruent to Z2 and Z2 is congruent to Z3, then Z1 is congruent to Z3. This property is commonly used in geometry to prove that congruent angles or segments are equal to each other.

Answer 2

The statement "If Z1 = Z2 and Z2 = Z3, then Z1 = Z3" is justified by the Reflexive Property of Congruence. So the correct option is D. Reflexive Property of Congruence

Step-by-step explanation:

According to Reflexive Property of Congruence any geometric figure or mathematical element is always congruent to itself. In the given scenario, if Z1 is congruent to Z2 and Z2 is congruent to Z3, then by the reflexive property, Z1 is also congruent to itself (Z1 = Z1). Therefore, Z1 must be congruent to Z3.

This property is a fundamental principle in geometry, ensuring that equality remains consistent within congruence relationships. It forms a basis for logical reasoning and deductions in geometry proofs. The Reflexive Property helps establish a clear and reliable foundation for congruence assertions, allowing mathematicians to make valid conclusions about the equality of angles, segments, or other geometric elements.

In summary, the statement provided aligns with the Reflexive Property of Congruence, asserting that when two angles are congruent to a third angle, they are also congruent to each other. This foundational property contributes to the coherence and validity of geometric reasoning and proofs. So the correct option is D. Reflexive Property of Congruence