Question

complete the proofs below by filling in the missing statements and reasons.

1. given: ∠1 and ∠2 form a linear pair; ∠1 ≅ ∠3

prove: ∠2 and ∠3 are supplementary

Explanation:

Step1: Identify the given information

• Statement 1: $\angle1$ and $\angle2$ form a linear pair (Given)
• Statement 4: $\angle1\cong\angle3$ (Given)

Step2: Use the definition of a linear pair

• Statement 2: $\angle1$ and $\angle2$ are supplementary (Def. of linear pair)
• Statement 3: $m\angle1 + m\angle2=180^{\circ}$ (Def. of supplementary)

Step3: Use substitution and congruent angles

• Statement 5: $m\angle1 = m\angle3$ (Def. of congruent angles)
• Statement 6: $m\angle3 + m\angle2=180^{\circ}$ (Substitution Theorem)

Step4: Use the definition of supplementary angles

• Statement 7: $\angle2$ and $\angle3$ are supplementary (Def. of supplementary)

Answer:

1. Given
2. Def. of linear pair
3. Def. of supplementary
4. Given
5. Def. of congruent angles
6. Substitution Theorem
7. Def. of supplementary