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. mTWX + mUTW = 180 2. _________________________________
3. mRTU + mUTW = 180 3. _________________________________
4. mTWX + mUTW = mRTU + mUTW 4. ____________________________
5. mTWX = mRTU 5. Subtraction property of equality
6. 𝑆𝑈⃡ || 𝑉𝑋⃡ 6. _________________________________
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)
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. mTWX + mUTW = 180 2. _________________________________
3. mRTU + mUTW = 180 3. _________________________________
4. mTWX + mUTW = mRTU + mUTW 4. ____________________________
5. mTWX = mRTU 5. Subtraction property of equality
6. 𝑆𝑈⃡ || 𝑉𝑋⃡ 6. _________________________________
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)
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