Question

segment ab is congruent to segment ab. this statement shows the ______ property.
reflexive
symmetric
transitive
substitution

Explanation:

To determine the property, we analyze each option:

• Reflexive property: A geometric figure (like a segment) is congruent to itself. For segment \( AB \), \( AB \cong AB \) fits this, as it states the segment is congruent to itself.
• Symmetric property: If \( A \cong B \), then \( B \cong A \). This is about order reversal, not self - congruence.
• Transitive property: If \( A \cong B \) and \( B \cong C \), then \( A \cong C \). It involves three figures, not self - congruence.
• Substitution property: Allows replacing a quantity with an equal/congruent one. It's not about a figure being congruent to itself.

So the reflexive property matches the statement \( \text{Segment } AB \text{ is congruent to segment } AB \).

Answer:

A. reflexive