Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. Prove: ∠1 ≅ ∠3 By definition of supplementary angles, m∠1 + m∠2 = _____ (a) and m∠2 + m∠3 = _____ (b). Then, m∠1 + m∠2 = m∠2 + m∠3 by the __________ (c). Subtract m∠2 from each side. You get m∠1 = ______ (d), or ∠1 ≅ _____ (e).
7 answers
By definition of supplementary angles, m∠1 + m∠2 = 180° (a) and m∠2 + m∠3 = 180° (b). Then, m∠1 + m∠2 = m∠2 + m∠3 by the Transitive Property of Equality (c). Subtract m∠2 from each side. You get m∠1 = m∠3 (d), or ∠1 ≅ ∠3 (e).
By definition of supplementary angles, m∠1 + m∠2 = 180° (a) and m∠2 + m∠3 = 180° (b). Then, m∠1 + m∠2 = m∠2 + m∠3 by the Transitive Property of Equality (c). Subtract m∠2 from each side. You get m∠1 = m∠3 (d), or ∠1 ≅ ∠3 (e).
Your original answer is correct. Here's the proof written out more formally:
Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary.
We are trying to prove: ∠1 ≅ ∠3
Proof:
By the definition of supplementary angles, we have:
m∠1 + m∠2 = 180° (a)
m∠2 + m∠3 = 180° (b)
Since ∠2 is common to both equations, we can equate them:
m∠1 + m∠2 = m∠2 + m∠3
Using the Transitive Property of Equality, we can simplify the equation to:
m∠1 = m∠3 (c)
This means that the measures of ∠1 and ∠3 are equal. By the definition of congruent angles, we can conclude that ∠1 ≅ ∠3.
Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary.
We are trying to prove: ∠1 ≅ ∠3
Proof:
By the definition of supplementary angles, we have:
m∠1 + m∠2 = 180° (a)
m∠2 + m∠3 = 180° (b)
Since ∠2 is common to both equations, we can equate them:
m∠1 + m∠2 = m∠2 + m∠3
Using the Transitive Property of Equality, we can simplify the equation to:
m∠1 = m∠3 (c)
This means that the measures of ∠1 and ∠3 are equal. By the definition of congruent angles, we can conclude that ∠1 ≅ ∠3.
What is the value of x? Justify each step. AC = 32
Without further information or context, it is not possible to determine the value of x or justify any steps. The given information of AC = 32 does not provide any information about x or the shape or diagram in which it is used. Please provide additional relevant information or context to solve for x.
Write a two-column proof. Given: 7y = 8x – 14; y = 6 Prove: x = 7
Statements Reasons
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1. 7y = 8x - 14 Given
2. y = 6 Given
3. 7(6) = 8x - 14 Substitution (Substitute y with 6 in statement 1)
4. 42 = 8x - 14 Simplification
5. 42 + 14 = 8x Addition (Add 14 to both sides of statement 4)
6. 56 = 8x Simplification
7. 56/8 = x Division (Divide both sides of statement 6 by 8)
8. 7 = x Simplification
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1. 7y = 8x - 14 Given
2. y = 6 Given
3. 7(6) = 8x - 14 Substitution (Substitute y with 6 in statement 1)
4. 42 = 8x - 14 Simplification
5. 42 + 14 = 8x Addition (Add 14 to both sides of statement 4)
6. 56 = 8x Simplification
7. 56/8 = x Division (Divide both sides of statement 6 by 8)
8. 7 = x Simplification
1 answer