Question

∠e and ∠g are supplementary and ∠f and ∠e are supplementary. complete the proof that ∠g ≅ ∠f.
1 ∠e and ∠g are supplementary given
2 ∠f and ∠e are supplementary given
3 m∠e + m∠g = 180° definition of supplementary angles
4 m∠f + m∠e = 180°
5 m∠e + m∠g = m∠f + m∠e
6 m∠g = m∠f properties of addition, subtraction, multiplication, and division
7 ∠g ≅ ∠f

Explanation:

Step1: Reason for statement 4

Definition of supplementary angles (since \(\angle F\) and \(\angle E\) are supplementary, the sum of their measures is \(180^{\circ}\))

Step2: Reason for statement 5

Transitive property of equality (if \(a + b=c + d\) and \(a = c\), here \(a=m\angle E\), \(b = m\angle G\), \(c=m\angle F\), \(d=m\angle E\))

Step3: Reason for statement 7

Definition of congruent angles (if \(m\angle G=m\angle F\), then \(\angle G\cong\angle F\))

Answer:

1. Definition of supplementary angles; 4. Definition of supplementary angles; 5. Transitive property of equality; 7. Definition of congruent angles.