Question

if tu = 6 units, what must be true? su + ut = rt rt + tu = rs rs + su = ru tu + us = rs

Explanation:

Step1: Analyze line - segment relationships

From the figure, we know that the points \(R\), \(T\), \(U\), and \(S\) are collinear. The length of \(RS = 24\) units and \(RT=12\) units. So \(TS=RS - RT=24 - 12 = 12\) units. Also, \(TU = 6\) units, then \(US=TS - TU=12 - 6 = 6\) units.

Step2: Check each option

• Option 1: \(SU+UT = RT\). Since \(SU = 6\) units, \(UT = 6\) units, and \(RT = 12\) units, \(SU + UT=6 + 6=12\) units, which is equal to \(RT\).
• Option 2: \(RT+TU = RS\). \(RT = 12\) units, \(TU = 6\) units, and \(RS = 24\) units. \(RT+TU=12 + 6 = 18

eq24\).

• Option 3: \(RS+SU = RU\). \(RS = 24\) units, \(SU = 6\) units, \(RU=RT + TU=12 + 6 = 18\) units, \(RS+SU=24 + 6=30

eq18\).

• Option 4: \(TU+US = RS\). \(TU = 6\) units, \(US = 6\) units, and \(RS = 24\) units. \(TU + US=6+6 = 12

eq24\).

Answer:

SU + UT = RT