Question

1. t is the midpoint of $overline{su}$.
2. $overline{st} cong overline{tu}$
3. $st = tu$
4. $7x = 3x + 20$
5. blank
6. $x = 5$

reasons:

1. blank
2. definition of midpoint
3. definition of congruent segments
4. blank
5. subtraction property of equality
6. blank

Explanation:

For Statement 1 (Reason):

Step1: Identify the given info

The problem states "T is the midpoint of \(\overline{SU}\)" as a given statement. So the reason for statement 1 is "Given".

For Statement 4 (Reason):

Step1: Recall previous steps

We know from step 3 that \(ST = TU\), and if we assume \(ST=7x\) and \(TU = 3x + 20\) (from the diagram or context), we substitute \(ST\) and \(TU\) with their expressions. So the reason is "Substitution (using \(ST = TU\) from step 3)".

For Statement 5 (Statement):

Step1: Apply Subtraction Property of Equality

Start with \(7x=3x + 20\). Subtract \(3x\) from both sides: \(7x-3x=3x + 20-3x\), which simplifies to \(4x = 20\).

For Statement 6 (Reason):

Answer:

Step1: Solve for x

From \(4x=20\), divide both sides by 4 (Division Property of Equality): \(\frac{4x}{4}=\frac{20}{4}\), so \(x = 5\). The reason is "Division Property of Equality".

Final Answers for each blank:

1. Given
2. Substitution (using \(ST = TU\))
3. \(4x=20\)
4. Division Property of Equality