Question

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 1

[AI-generated answer — Bot GPT 3.5]

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

[AI-generated answer — Bot GPT 3.5]

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)

Answer 4

[AI-generated answer — Explain Bot]

To complete the proof, you can use the properties of supplementary angles and the subtraction property of equality. Here's how you can fill in the missing steps:

1. Given: ∠TWX and ∠UTW are supplementary
2. ∠TWX and ∠UTW are supplementary [Given]
3. m∠TWX + m∠UTW = 180 [Definition of supplementary angles]
4. m∠RTU + m∠UTW = 180 [Substitution, using ∠TWX and ∠UTW]
5. m∠TWX + m∠UTW = m∠RTU + m∠UTW [Transitive property of equality]
6. m∠TWX = m∠RTU [Subtraction property of equality]
7. ∠SUT || ∠VX [Alternate interior angles are congruent]

So, the proof can be completed by stating:
Prove: ∠SUT || ∠VX
Statement Reason
1. ∠TWX and ∠UTW are supplementary Given
2. m∠TWX + m∠UTW = 180 Definition of supplementary angles
3. m∠RTU + m∠UTW = 180 Substitution, using ∠TWX and ∠UTW
4. m∠TWX + m∠UTW = m∠RTU + m∠UTW Transitive property of equality
5. m∠TWX = m∠RTU Subtraction property of equality
6. ∠SUT || ∠VX Alternate interior angles are congruent