Question

what is the missing reason in the proof?
a. segment addition
b. congruent segments theorem
c. transitive property of equality
d. subtraction property of equality

Explanation:

To determine the missing reason in a proof, we analyze each option:

• Option A (Segment Addition): Applies when adding segments (e.g., \( AB + BC = AC \)), not for equality properties.
• Option B (Congruent Segments Theorem): Relates to congruent segments (length equality), not a general equality property.
• Option C (Transitive Property of Equality): States if \( a = b \) and \( b = c \), then \( a = c \). Often used in proofs with equalities.
• Option D (Subtraction Property of Equality): Applies when subtracting from both sides (e.g., if \( a = b \), then \( a - c = b - c \)), not transitive.

Assuming the proof involves equalities linked transitively, the Transitive Property of Equality is the most appropriate.

Answer:

C. Transitive Property of Equality