The two column proof showing that m∠5 + m∠2 + m∠6 = 180° is as detailed below.
How to use two column proof?
A two-column proof is defined as geometric proof that consists of a list of statements, and then the reasons that we know those statements are true.
Thus, the two column proof is;
Statement 1: y || z
Reason 1: Given
Statement 2: m∠1 + m∠2 + m∠3 = m∠LAM
Reason 2: Angle addition postulate
Statement 3: m∠1 + m∠2 + m∠3 = 180°
Reason 3: definition of straight angle
Statement 4: ∠1 ≅ ∠5
Reason 4: Alternate interior angles theorem
Statement 5: ∠3 ≅ ∠6
Reason 5: Alternate interior angles theorem
Statement 6: m∠1 ≅ m∠5
Reason 6: Definition of ≅(congruency)
Statement 7: ∠3 ≅ ∠6
Reason 7: Definition of ≅(congruency)
Statement 8: m∠5 + m∠2 + m∠6 = 180°
Reason 8: substitution
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