Question

1. given: ∠1 and ∠4 form a linear pair; ∠1 and ∠2 are supplementary. prove: ∠3≅∠4. statements reasons 1. ∠1 and ∠4 form a linear pair 1. 2. 2. supplement theorem 3. 3. given 4. 4. congruent supplements theorem 5. ∠2≅∠3 5. 6. 6. transitive property

Explanation:

Step1: State given fact

Given

Step2: State supplementary relationship

$\angle1$ and $\angle4$ are supplementary

Step3: State other given

$\angle1$ and $\angle2$ are supplementary

Step4: Apply congruent - supplements theorem

Since $\angle1$ is supplementary to both $\angle4$ and $\angle2$, $\angle2\cong\angle4$

Step5: Vertical - angles are congruent

Vertical - angles theorem

Step6: Prove $\angle3\cong\angle4$

Since $\angle2\cong\angle3$ (vertical angles) and $\angle2\cong\angle4$, then $\angle3\cong\angle4$ by transitive property

Answer:

1. Given
2. $\angle1$ and $\angle4$ are supplementary
3. $\angle1$ and $\angle2$ are supplementary
4. $\angle2\cong\angle4$
5. Vertical - angles theorem
6. $\angle3\cong\angle4$