Question

1. complete the reasons for the 2 - column proof. given: ∠1 and ∠2 are complementary ∠3 and ∠4 are complementary prove: ∠1≅∠4 statements reasons 1. ∠1 and ∠2 are complementary ∠3 and ∠4 are complementary 1. 2. m∠1 + m∠2 = 90° 2. 3. m∠3 + m∠4 = 90° 3. 4. ∠2≅∠3 4. 5. m∠2 = m∠3 5. 6. m∠1 + m∠2 = m∠3 + m∠4 6. 7. m∠1 + m∠3 = m∠3 + m∠4 7. 8. m∠1 = m∠4 8. 9. ∠1≅∠4 9.

Explanation:

Step1: Given information

Given

Step2: Definition of complementary angles

Definition of complementary angles

Step3: Definition of complementary angles

Definition of complementary angles

Step4: Vertical - angles are congruent

Vertical - angles are congruent

Step5: Definition of congruent angles

Definition of congruent angles

Step6: Transitive property of equality

Transitive property of equality

Step7: Substitution property of equality

Substitution property of equality

Step8: Subtraction property of equality

Subtraction property of equality

Step9: Definition of congruent angles

Definition of congruent angles

Answer:

1. Given
2. Definition of complementary angles
3. Definition of complementary angles
4. Vertical - angles are congruent
5. Definition of congruent angles
6. Transitive property of equality
7. Substitution property of equality
8. Subtraction property of equality
9. Definition of congruent angles