Question

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

1 ∠r and ∠s are supplementary given
2 ∠t and ∠r are supplementary given
3 m∠r + m∠s = 180°
4 m∠t + m∠r = 180°
5 m∠r + m∠s = m∠t + m∠r transitive property of equality
6 m∠t = m∠s properties of addition, subtraction, multiplication, and division
7 ∠t ≅ ∠s

Explanation:

Step1: Definition of supplementary angles

If two angles are supplementary, the sum of their measures is \(180^{\circ}\). So for \(\angle R\) and \(\angle S\) being supplementary, \(m\angle R + m\angle S=180^{\circ}\) (by the definition of supplementary angles).

Step2: Definition of supplementary angles

Since \(\angle T\) and \(\angle R\) are supplementary, \(m\angle T + m\angle R = 180^{\circ}\) (by the definition of supplementary angles).

Step3: Definition of congruent angles

If \(m\angle T=m\angle S\), then \(\angle T\cong\angle S\) (by the definition of congruent angles: two angles are congruent if their measures are equal).

Answer:

1. Definition of supplementary angles; 4. Definition of supplementary angles; 7. Definition of congruent angles.