The two column proof of the given angles are as detailed below with all statements and reasons.
How to carry out a two column proof?
From the given diagram, we are shown that;
Statement 1; a II b
Reason 1; Given
Statement 2; ∠1 ≅ ∠2
Reason2 ; Given
Now, from the transversal line theorem, we know that If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Similarly, If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
Thus;
Statement 3; ∠1 = ∠4
Reason 3; Transversal Line theorem
Statement 4; ∠2 = ∠3
Reason 4; Alternate angles
Statement 5; ∠3 ≅ ∠4
Reason 5; Substitution Property
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