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Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f

Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorme
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?

A. vertical angles theorem
B. alternate exterior angles theorem
C. converse corresponding angles theorem
D. converse alternate interior angles theorem

Given g h and 2 3 Prove e f Statements Reasons 1 g h 1 given 2 1 2 2 corresponding angles theorme 3 2 3 3 given 4 1 3 4 transitive property 5 e f 5 What is the class=

Respuesta :

Answer:  Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Given: g ∥ h and ∠2 ≅ ∠3

    Statements                               Reasons

1. g || h                               1. given

2. ∠1 ≅ ∠2                               2.corresponding angles theorem

3. ∠2 ≅ ∠3                               3. given

4. ∠1 ≅ ∠3                                4. transitive property

5. e || f                                      5. Converse alternate interior angles.

As we know that if alternate angles are equal then two lines would be parallel using converse alternate interior angles.

Hence, Option 'D' is correct.

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