Question

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

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

Explanation:

Step1: Given

Given in the problem statement.

Step2: Given

Given in the problem statement.

Step3: Definition of supplementary angles

If two angles are supplementary, their measures add up to \(180^{\circ}\).

Step4: Definition of supplementary angles

If two angles are supplementary, their measures add up to \(180^{\circ}\).

Step5: Transitive property of equality

Since \(m\angle S + m\angle U=180^{\circ}\) and \(m\angle S + m\angle T = 180^{\circ}\), then \(m\angle S + m\angle U=m\angle S + m\angle T\).

Step6: Subtraction property of equality

Subtract \(m\angle S\) from both sides of \(m\angle S + m\angle U=m\angle S + m\angle T\).

Step7: Definition of congruent angles

If \(m\angle T = m\angle U\), then \(\angle T\cong\angle U\).

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