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. linear pair (supplement) theorem 3. 3. given 4. 4. congruent supplements theorem 5. ∠2≅∠3 5. 6. 6. transitive property

Explanation:

Step1: State given fact

1. $\angle1$ and $\angle4$ form a linear pair (Given)

Step2: Apply linear - pair theorem

1. $\angle1$ and $\angle4$ are supplementary (Linear Pair (Supplement) Theorem)

Step3: State second given fact

1. $\angle1$ and $\angle2$ are supplementary (Given)

Step4: Use congruent - supplements theorem

1. $\angle2\cong\angle4$ (Congruent Supplements Theorem)

Step5: Vertical angles are congruent

1. $\angle2\cong\angle3$ (Vertical Angles Theorem)

Step6: Use transitive property

1. $\angle3\cong\angle4$ (Transitive Property)

Answer:

Statements	Reasons
2. $\angle1$ and $\angle4$ are supplementary	2. Linear Pair (Supplement) Theorem
3. $\angle1$ and $\angle2$ are supplementary	3. Given
4. $\angle2\cong\angle4$	4. Congruent Supplements Theorem
5. $\angle2\cong\angle3$	5. Vertical Angles Theorem
6. $\angle3\cong\angle4$	6. Transitive Property