Final Answer:
1. Statement: $\frac{v+9}{3} = 8$ — Reason: Given
Statement: $v + 9 = 24$ — Reason: Multiply both sides by 3 (Multiplication Property of Equality)
Statement: $v = 15$ — Reason: Subtract 9 from both sides (Subtraction Property of Equality)
2. Statement: $2(n + 5) = -2$ — Reason: Given
Statement: $n + 5 = -1$ — Reason: Divide both sides by 2 (Division Property of Equality)
Statement: $n = -6$ — Reason: Subtract 5 from both sides (Subtraction Property of Equality)
3. Statements & Reasons:
1. ∠1 and ∠3 are a linear pair; ∠2 and ∠3 are a linear pair. — Reason: Given
2. ∠1 and ∠3 are supplementary angles; ∠2 and ∠3 are supplementary angles. — Reason: Definition of linear pair (linear pairs form a straight line → sum to 180°)
3. ∠1 ≅ ∠2 — Reason: If two angles are supplementary to the same angle, they are congruent (Congruent Supplements Theorem)
4. $m\angle 1 = m\angle 2$ — Reason: Definition of congruent angles
4. Statements & Reasons:
1. $AB = BC$ — Reason: Given
2. $AC = AB + BC$ — Reason: Segment Addition Postulate (B is between A and C)
3. $AC = BC + BC$ — Reason: Substitution (replace AB with BC using statement 1)
4. $AC = 2BC$ — Reason: Simplify (combine like terms)
5. $\frac{1}{2}AC = BC$ — Reason: Divide both sides by 2 (Division Property of Equality)
Parent Tip: Review the logic above to help your child master the concept of geometry proofs worksheets two column.
