Question

Plz Help 60 points!!!!

Provide reasons for the proof. Given: ∠2 ≅ ∠4 and ∠2 and ∠3 are supplementary Prove: ∠1 ≅ ∠3

Answer 1

Statement Reason

1. 2  4 1. Given

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

3. 2 and 3 are supplementary 3. Given

4. m2 + m3 = 180 4. Definition of supplementary angles

5. 1 and 4 are supplementary 5. Given

6. m1 + m4 = 180 6. Definition of supplementary angles

7. m1 + m4 = m2 + m3 7. transitive property of equality

8. m1 + m4 = m4 + m3 8. substitution property

9. m1 = m3 9. subtraction property

10. 1  3 10. converse of angles congruence postulate

Answer 2

7.By transitive property of equality

8.By substitution property

9.Subtraction property of equality

10.Converse of angles congruence postulate.

Explanation:

We are given that

`\angle 2\cong \angle 4` , angle 2 and angle 3 are supplementary and angle 1 and angle 4 are supplementary.

We have to prove that
`\angle 1\cong\angle 3`

We have to write missing statements in given proof.

1.
`\angle 2\cong\angle 4`

Given

2.
`m\angle 2=m\angle 4`

Angle congruence postulate

3.Angle 2 and angle 3 are supplementary.

Given

4.
`m\angle 2+m\angle 3=180^(\circ)`

By definition of supplementary angles

5.Angle 1 and angle 4 are supplementary

Given

6.
`m\angle 1+m\angle 4=180^(\circ)`

By definition of supplementary angles

7.
`m\angle 1+m\angle 4=m\angle 2+m\angle 3`

By transitive property of equality

8.
`m\angle 1+m\angle 4=m\angle 4+m\angle 3`

By substitution property

9.
`m\angle 1=m\angle 3`

Subtraction property of equality

10.
`m\angle 1\cong m\angle 3`

Converse of angle congruence postulate