The reasons for the proofs are
1. GE || JH Given
2. ∠3 ≅ ∠1 Corresponding angles
3. ∠1 ≅ ∠2 Given
4. ∠3 ≅ ∠2 Substitution property
5. AB||GD Alternate exterior angles
Proof of parallel lines
From the question, we are to provide reasons for the proof
From the diagram,
we can observe that ∠3 and ∠1 are corresponding angles on the parallel lines GE and JH
∴ ∠3 ≅ ∠1 (Corresponding angles)
Also,
Since ∠1 ≅ ∠2 (Given)
Then,
∠3 ≅ ∠2 by the substitution property
Now,
∠3 and ∠2 are alternate exterior angles of lines AB and GD
Since ∠3 ≅ ∠2
∴Lines AB and GD are parallel lines
Hence,
1. GE || JH Given
2. ∠3 ≅ ∠1 Corresponding angles
3. ∠1 ≅ ∠2 Given
4. ∠3 ≅ ∠2 Substitution property
5. AB||GD Alternate exterior angles
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