Question

complete the proofs below by filling in the missing statements and reasons. 10. given: ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary prove: ∠2≅∠3 statements reasons 1. ∠1 and ∠2 form a linear pair 1. given 2. ∠1 and ∠2 are supplementary 2. linear pair postulate 3. m∠1 + m∠2 = 180° 3. def of supplementary angles 4. ∠1 and ∠3 are supplementary 4. given 5. m∠1 + m∠3 = 180° 5. def of supp angles 6. m∠1 + m∠2 = m∠1 + m∠3 6. substitution property 7. m∠2 = m∠3 7. subtraction property of equality 8. ∠2≅∠3 8. definition of congruent angles © gina wilson (all things algebra), 2014

Explanation:

Step1: State given fact

Given

Step2: Apply linear - pair postulate

Linear pair postulate

Step3: Use definition of supplementary angles

Definition of supplementary angles

Step4: State given fact

Given

Step5: Use definition of supplementary angles

Definition of supplementary angles

Step6: Substitute equal - sums

Substitution property

Step7: Subtract \(m\angle1\) from both sides

Subtraction property of equality

Step8: Use definition of congruent angles

Definition of congruent angles

Answer:

1. Given
2. Linear pair postulate
3. Definition of supplementary angles
4. Given
5. Definition of supplementary angles
6. Substitution property
7. Subtraction property of equality
8. Definition of congruent angles