Question

(Geometry) Provide reasons for the proof

Answer 1

Answer:

Complete proof is shown below.

Step-by-step explanation:

Given information: $\angle 2\cong \angle 4$ and ∠2 and ∠3 are supplementary angles.

To prove : $\angle 1\cong \angle 3$

Proof:

Statement                                       Reason

1. ∠2 ≅ ∠4                                      1. Given

2. m∠2 = m∠4                                2. Angle congruence postulate

3. ∠2 and ∠3 are supplementary angles          3. Given

4. m∠2 + m∠3 = 180°                      4. Definition of supplementary angles

5. ∠1 and ∠4 are supplementary angles           5. Linear pairs

6. m∠1 + m∠4 = 180°                       6. Definition of supplementary angles

7. m∠1 + m∠4 = m∠2 + m∠3           7. Substitution property of equality

8. m∠1 + m∠4 = m∠4 + m∠3           8. Substitution property of equality

9. m∠1 =  m∠3                                 9. Subtraction property of equality

10. m∠1 ≅  m∠3                               10. Angle congruence postulate

Answer 2

Answer:

5 is given

7 Angle congreunce postulate

8 angle congreunce postulate

9 given

10 is given