Complete the proof (U4L3 or IXL G-D.7)

Question

Given TWX and UTW are supplementary
Prove: 𝑺𝑼⃡ || 𝑽𝑿⃡
Statement Reason
1. TWX and UTW are supplementary 1. _______________________
2. mTWX + mUTW = 180 2. _________________________________
3. mRTU + mUTW = 180 3. _________________________________
4. mTWX + mUTW = mRTU + mUTW 4. ____________________________
5. mTWX = mRTU 5. Subtraction property of equality
6. 𝑆𝑈⃡ || 𝑉𝑋⃡ 6. _________________________________

Answer 1

1. Given: ∠TWX and ∠UTW are supplementary.
2. Definition of Supplementary Angles: Supplementary angles add up to 180 degrees.
3. ∠TWX + ∠UTW = 180 degrees. (From statement 1 and definition of supplementary angles)
4. ∠RTU + ∠UTW = 180 degrees. (Because ∠TWX and ∠UTW are supplementary)
5. Substitution Property of Equality: If two quantities are equal to a third quantity, then they are equal to each other.
Thus, ∠TWX + ∠UTW = ∠RTU + ∠UTW.
6. Subtract ∠UTW from both sides: ∠TWX = ∠RTU.
7. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Thus, SU || VX. (Based on the fact that ∠TWX = ∠RTU and the definition of parallel lines)

Answer 2

Complete the proof (U4L3 or IXL G-D.7)
Given TWX and UTW are supplementary
Prove: 𝑺𝑼⃡ || 𝑽𝑿⃡
Statement Reason
1. TWX and UTW are supplementary 1. _______________________
2. mTWX + mUTW = 180 2. _________________________________
3. mRTU + mUTW = 180 3. _________________________________
4. mTWX + mUTW = mRTU + mUTW 4. ____________________________
5. mTWX = mRTU 5. Subtraction property of equality
6. 𝑆𝑈⃡ || 𝑉𝑋⃡ 6. _________________________________

Answer 3

1. Given: ∠TWX and ∠UTW are supplementary.
2. Definition of Supplementary Angles: Supplementary angles add up to 180 degrees.
3. ∠TWX + ∠UTW = 180 degrees. (From statement 1 and definition of supplementary angles)
4. ∠RTU + ∠UTW = 180 degrees. (Because ∠TWX and ∠UTW are supplementary)
5. Addition Property of Equality: If two quantities are equal to a third quantity, then they are equal to each other.
∠TWX + ∠UTW = ∠RTU + ∠UTW.
6. Subtract ∠UTW from both sides: ∠TWX = ∠RTU.
7. Alternate Interior Angles Theorem: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
Thus, SU || VX. (Based on the fact that ∠TWX and ∠RTU are congruent and the Alternate Interior Angles Theorem)