Subjects geometry

Segment Ef Length F4D8E6

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Question: Which of the following constructions represents $\overline{EF}$ which has a length equal to $3AB + CD$?
1. **Problem Statement:** We need to find a segment $\overline{EF}$ such that its length is equal to $3AB + CD$. 2. **Understanding the problem:** The length $3AB + CD$ means the segment $EF$ is composed of three times the length of segment $AB$ plus the length of segment $CD$. 3. **Formula:** $$EF = 3 \times AB + CD$$ 4. **Interpreting the options:** - Option 1: $EF$ has one arc mark, so it likely equals $AB$. - Option 2: $EF$ has two arc marks, so it likely equals $2AB$. - Option 3: $EF$ has two arc marks plus a longer segment, possibly $2AB + CD$. - Option 4: $EF$ has three arc marks and the longest segment, likely $3AB + CD$. 5. **Conclusion:** The correct construction for $EF = 3AB + CD$ is the one with three arc marks plus the segment $CD$, which corresponds to **Option 4**. **Final answer:** Option 4 represents $\overline{EF}$ with length $3AB + CD$.