Question

1. which property justifies the following statement? (overline{ab} cong overline{ab})

• transitive property of congruence
• distributive property of congruence
• reflexive property of congruence
• symmetric property of congruence

Explanation:

The Reflexive Property of Congruence states that any geometric figure (like a segment \(\overline{AB}\)) is congruent to itself. The statement \(\overline{AB} \cong \overline{AB}\) shows a segment is congruent to itself, which matches the Reflexive Property. The Transitive Property involves three figures (\(a \cong b\), \(b \cong c\) implies \(a \cong c\)), the Distributive Property is for operations (not congruence), and the Symmetric Property is \(a \cong b\) implies \(b \cong a\), none of which fit here.

Answer:

Reflexive Property of Congruence