The proof that is not needed John's proof is When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent
The following proof are needed.
- When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. This is why ∠4≅∠1 and ∠5≅∠3.
- The sum of the angles on one side of a straight line is 180. That is why m∠4 + m∠2 + m∠5 = 180°
- If a statement about a is true and a = b statement formed by replacing a with b is also true.
m∠4 + m∠2 + m∠5 = 180° (sum of angles on a straight line)
∠4≅∠1 and ∠5≅∠3 (alternate interior angles)
Therefore,
∠1 can replace ∠4 and ∠3 can replace ∠5
m∠1 + m∠2 + m∠3 = 180°
Therefore, When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent is not needed.
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