Question

∠u and ∠s are supplementary and ∠t and ∠s are supplementary. complete the proof that ∠t ≅ ∠u.

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

Explanation:

Step1: Identify Given Info

Statement 1: Given (∠U and ∠S supplementary)

Step2: Identify Given Info

Statement 2: Given (∠T and ∠S supplementary)

Step3: Define Supplementary

Statement 3: Definition of supplementary angles (supplementary angles sum to \(180^\circ\))

Step4: Define Supplementary

Statement 4: Definition of supplementary angles (supplementary angles sum to \(180^\circ\))

Step5: Transitive Property

Statement 5: Transitive property of equality (since both equal \(180^\circ\), they equal each other)

Step6: Subtract \(m\angle S\)

Statement 6: Subtraction property of equality (subtract \(m\angle S\) from both sides)

Step7: Define Congruent Angles

Statement 7: Definition of congruent angles (angles with equal measure are congruent)

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