Question

choose the property that justifies each statement below. possible points: 33.33 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 by 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"

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

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

-6y and -y are combined, which is simplification by combining like - terms (but among given options, substitution as we are essentially replacing -6y - y with -7y).

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

Both sides are divided by 5, so it's division.

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

The equality is reversed, so it's symmetric.

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. Substitution
5. Division
6. Symmetric
7. Definition of Congruence