Question

if $rs = st$ and $st = tu$, which property justifies $rs = tu$?
image of a line segment with points r, s, t, u in order

• reflexive property
• transitive property
• substitution property
• addition property of equality

Explanation:

The Transitive Property of Equality states that if \( a = b \) and \( b = c \), then \( a = c \). Here, \( RS = ST \) (so \( a = RS \), \( b = ST \)) and \( ST = TU \) (so \( b = ST \), \( c = TU \)), so by the Transitive Property, \( RS = TU \). The Reflexive Property is \( a = a \), Substitution is replacing a value, and Addition Property of Equality involves adding to both sides, which don't apply here.

Answer:

B. Transitive Property (assuming the options are labeled with the second option as Transitive Property; if the options are ordered as given, the second option: Transitive Property)