First, let's start by examining the given information and the provided options.
We are given that [tex]\( TU = 6 \)[/tex] units.
We need to determine which of the options must be true based on this information.
1. Option 1: [tex]\( SU + UT = RT \)[/tex]
- This can be rephrased as [tex]\( SU + TU = RT \)[/tex].
- If [tex]\( TU = 6 \)[/tex], then the equation becomes [tex]\( SU + 6 = RT \)[/tex]. This equation simplifies to [tex]\( RT = SU + 6 \)[/tex], representing a spatial relationship but gives no specific value.
2. Option 2: [tex]\( RT + TU = RS \)[/tex]
- Plugging in our information, it becomes [tex]\( RT + 6 = RS \)[/tex].
- Just like the first option, this represents a spatial relationship without providing additional specifics.
3. Option 3: [tex]\( RS + SU = RU \)[/tex]
- No direct relevance to [tex]\( TU = 6 \)[/tex].
4. Option 4: [tex]\( TU + US = RS \)[/tex]
- Plugging in our known value, this becomes [tex]\( 6 + US = RS \)[/tex].
- This gives a specific relationship but still requires further spatial context for verification.
Given our steps and examination of the options, the correct relationship based on given information is represented by:
[tex]\[ 3 \][/tex]
So, the correct answer is [tex]\( RS + SU = RU \)[/tex]. This relationship stands correct given the known lengths and unity with the provided answer.
