Subtraction Property of EqualitySupplementary angles add up to 180.∠’s with the same measures are ≅.Transitive Property of Equality

Question

Examine each statement and reason in the two-column proof.

Given:
∠1
and ∠2
are supplementary
∠2
and ∠3
are supplementary
Prove:
∠1
and ∠3

Fill-in the missing statements by moving the correct answer to the empty boxes.

Statements Reason
1. ∠1 and ∠2 are supplementary 1. Given
2. m∠1 + m∠2 = 180 2. Supplementary angles add up to 180.
3. ∠2 and ∠3 are supplementary 3. Given
4. m∠2 + m∠3 = 180 4. Supplementary angles add up to 180.
5. m∠1 + m∠2 = m∠2 + m∠3 5. Transitive Property of Equality
6. m∠1 = m∠3 6.
7. ∠1 ≅ ∠3 7.

Answer 1

Here’s the completed two-column proof with the missing statements filled in:

Statements | Reason --- | ---

1. ∠1 and ∠2 are supplementary | 1. Given
2. m∠1 + m∠2 = 180 | 2. Supplementary angles add up to 180.
3. ∠2 and ∠3 are supplementary | 3. Given
4. m∠2 + m∠3 = 180 | 4. Supplementary angles add up to 180.
5. m∠1 + m∠2 = m∠2 + m∠3 | 5. Transitive Property of Equality
6. m∠1 = m∠3 | 6. Subtraction Property of Equality
7. ∠1 ≅ ∠3 | 7. Definition of Congruent Angles

This proof demonstrates the relationships between the angles based on their measures and utilizes properties of equality and definitions related to congruence.