Question

∠w and ∠u are supplementary and ∠u and ∠v are supplementary. complete the proof that ∠w ≅ ∠v.

	statement	reason
1	∠w and ∠u are supplementary
2	∠u and ∠v are supplementary
3	m∠w + m∠u = 180°
4	m∠u + m∠v = 180°
5	m∠w + m∠u = m∠u + m∠v
6	m∠w = m∠v
7	∠w ≅ ∠v

Explanation:

Step1: Reason for Statement 1

Given (as per the problem statement, ∠W and ∠U are supplementary is given)

Step2: Reason for Statement 2

Given (as per the problem statement, ∠U and ∠V are supplementary is given)

Step3: Reason for Statement 3

Definition of supplementary angles (if two angles are supplementary, their measures sum to \(180^\circ\))
\(m\angle W + m\angle U = 180^\circ\)

Step4: Reason for Statement 4

Definition of supplementary angles (if two angles are supplementary, their measures sum to \(180^\circ\))
\(m\angle U + m\angle V = 180^\circ\)

Step5: Reason for Statement 5

Transitive property of equality (since \(m\angle W + m\angle U = 180^\circ\) and \(m\angle U + m\angle V = 180^\circ\), we can set them equal to each other)
\(m\angle W + m\angle U = m\angle U + m\angle V\)

Step6: Reason for Statement 6

Subtraction property of equality (subtract \(m\angle U\) from both sides of \(m\angle W + m\angle U = m\angle U + m\angle V\))
\(m\angle W = m\angle V\)

Step7: Reason for Statement 7

Definition of congruent angles (if two angles have equal measures, they are congruent)
\(\angle W \cong \angle V\)

Answer:

1. Given
2. Given
3. Definition of supplementary angles
4. Definition of supplementary angles
5. Transitive property of equality
6. Subtraction property of equality
7. Definition of congruent angles