Questions: Fill in the blanks to complete the two-column proof. Given T is the midpoint of SU. Prove x=5 STATEMENT 1. T is the m 2. ST ≅ TU REASONS 1. 2. Definition of midpoint 3. ST=TU 3. Definition of congruent segments 4. 7x=3x+20 4. 5. C 6. x=5 5. Subtraction Property of Equality 6.

Fill in the blanks to complete the two-column proof. Given T is the midpoint of SU. Prove x=5 STATEMENT 1. T is the m 2. ST ≅ TU REASONS 1. 2. Definition of midpoint 3. ST=TU 3. Definition of congruent segments 4. 7x=3x+20 4. 5. C 6. x=5 5. Subtraction Property of Equality 6.
Transcript text: Fill in the blanks to complete the two-column proof. Given $T$ is the midpoint of $\overline{S U}$. Prove $x=5$ STATEMEN 1. $T$ is the m 2. $\overline{S T} \cong \overline{T U}$ REASONS 1. $\qquad$ 2. Definition of midpoint 3. $S T=T U$ 3. Definition of congruent segments 4. $7 x=3 x+20$ 4. $\qquad$ 5. C $\qquad$ 6. $x=5$ 5. Subtraction Property of Equality 6. $\qquad$
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Solution

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Solution Steps

Step 1: Given Information

Statement: \( T \) is the midpoint of \( \overline{SU} \).
Reason: Given.

Step 2: Definition of Midpoint

Statement: \( \overline{ST} \cong \overline{TU} \).
Reason: Definition of midpoint.

Step 3: Definition of Congruent Segments

Statement: \( ST = TU \).
Reason: Definition of congruent segments.

Step 4: Substitute Segment Lengths

Statement: \( 7x = 3x + 20 \).
Reason: Substitution.

Step 5: Solve for \( x \)

Statement: \( 4x = 20 \).
Reason: Subtraction Property of Equality.

Step 6: Final Answer

Statement: \( x = 5 \).
Reason: Division Property of Equality.

Final Answer

\( x = 5 \)

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