Question

vi given: ∠1 and ∠2 are supplementary prove: ∠3 and ∠4 are supplementary 1. __________, 1. given 2. ________, 2. def. of supplementary angles 3. ________, 3. vertical angles are congruent 4. ________, 4. def. of congruent angles 5. ________, 5. substitution 6. ________, 6. def. of __________

Explanation:

Step1: State the given fact

$\angle1$ and $\angle2$ are supplementary

Step2: Write the definition of supplementary angles

$m\angle1 + m\angle2=180^{\circ}$

Step3: Note vertical - angle congruence

$\angle1\cong\angle3$ and $\angle2\cong\angle4$ (Vertical angles are congruent)

Step4: Write the definition of congruent angles

$m\angle1 = m\angle3$ and $m\angle2 = m\angle4$

Step5: Substitute the angle - measure equalities

$m\angle3 + m\angle4=180^{\circ}$

Step6: Use the definition of supplementary angles

$\angle3$ and $\angle4$ are supplementary

Answer:

1. $\angle1$ and $\angle2$ are supplementary
2. $m\angle1 + m\angle2 = 180^{\circ}$
3. $\angle1\cong\angle3,\angle2\cong\angle4$
4. $m\angle1 = m\angle3,m\angle2 = m\angle4$
5. $m\angle3 + m\angle4=180^{\circ}$
6. supplementary angles