Question

be ≅ de; select a reason...; search for reasons...; reflexive property; transitive property; substitution; in a triangle, sides opposite of congruent angles are congruent

Explanation:

Step1: Analyze the given information

We have a diagram where \( BE \cong DE \), and we need to select a reason for this congruence. The options are Reflexive Property, Transitive Property, Substitution, and "In a triangle, sides opposite of congruent angles are congruent".

Step2: Evaluate each option

• Reflexive Property: States that a segment is congruent to itself (\( BE \cong BE \)), not applicable here as we have \( BE \cong DE \).
• Transitive Property: Deals with if \( a \cong b \) and \( b \cong c \), then \( a \cong c \), not relevant here.
• Substitution: Involves replacing a value or expression, not related to segment congruence based on triangle angle - side relationships.
• "In a triangle, sides opposite of congruent angles are congruent": If in a triangle, the angles opposite \( BE \) and \( DE \) are congruent, then \( BE \cong DE \). This is the most logical reason for the congruence of two different segments \( BE \) and \( DE \) in a triangle context (implied by the diagram and the nature of the problem).

Answer:

In a triangle, sides opposite of congruent angles are congruent