Question

choose the property that justifies each statement below. if a = 2 and a + b = 3, then 2 + b = 3. if ∠3 ≅ ∠8 and ∠8 ≅ ∠10, then ∠3 ≅ ∠10. if 4(m + 6) = 32, then 4m + 24 = 32. if -6y + 10 - y = 0, then -7y + 10 = 0. if 5x = 15, then x = 3. if m∠k = 25°, then 25° = m∠k. if (overline{ab}congoverline{dc}), then ab = dc. definition of congruence; division; substitution; transitive; substitution; symmetric; distribution

Explanation:

Step1: Analyze "If a = 2 and a + b = 3, then 2 + b = 3"

Since a is replaced with 2, it's Substitution.

Step2: Analyze "If ∠3 ≅ ∠8 and ∠8 ≅ ∠10, then ∠3 ≅ ∠10"

This follows the Transitive property of congruence.

Step3: Analyze "If 4(m + 6) = 32, then 4m + 24 = 32"

The 4 is distributed over (m + 6), so it's Distribution.

Step4: Analyze "If -6y + 10 - y = 0, then -7y + 10 = 0"

Combining like - terms (-6y and -y), but not a named property in the list. However, if we consider basic algebraic simplification, it's not one of the given options in a strict sense. But if we assume we are just looking at the form - it's not one of the named properties.

Step5: Analyze "If 5x = 15, then x = 3"

Dividing both sides by 5, it's Division.

Step6: Analyze "If m∠K = 25°, then 25° = m∠K"

This is the Symmetric property.

Step7: Analyze "If $\overline{AB}\cong\overline{DC}$, then AB = DC"

This is the Definition of Congruence for line - segments.

Answer:

1. Substitution
2. Transitive
3. Distribution
4. (No correct option from the list in a strict sense)
5. Division
6. Symmetric
7. Definition of Congruence