Given: Segment \( A C \) has a length of 24 units, point \( B \) lies somewhere on segment \( A C \), and the length of segment \( B C \) is 6 units. Prove: \( A B=18 \) Statement: 1. Point \( B \) lies on segment \( A C \) Reason: 2. \( A B+B C=A C \) 3. \( \mathrm{AC}=24 \) 4. \( B C=6 \) 5. \( A B+6=24 \) 6. \( A B=18 \) 2. Postulate 3. Given 4. Given 1. Given 5. [ ? 6. \( \square \) Select the reason that best supports Statement 5 in the given proof. Subtraction Property of Equality Substitution Division Property of Equality

The reason that best supports Statement 5 in the given proof is the **Substitution**. This is because you are substituting the value of \( BC \) from Statement 4 into the equation in Statement 2 to solve for \( AB \). By replacing \( BC \) with 6, you arrive at \( AB + 6 = AC \), verifying the relationship between the segments. Now, when you find \( AB \) by isolating it, that's where the substitution plays a key role as the value of \( AC \) (24) is substituted back in. For a fun fact, did you know that the concept of segments and proofs is foundational in geometry? Ancient civilizations like the Greeks developed these concepts, with Euclid's "Elements" being one of the earliest and most influential works in mathematics, establishing the logical structure that underpins modern geometry! For more engagement, if you love puzzles, dive into some geometry challenges available in competitive math resources. Understanding how segments interact can really sharpen your problem-solving skills. Try proving various cases, working your way through complex figures, and don't shy away from testing different lengths and relationships!