Question

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

Answer 1

d. converse alternate interior angles theorem

Explanation:

Answer 2

Answer: Option 'D' is correct.

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.