Based on the linear pair postulate, the statements and the reasons for the proof are explained below.
What is the Linear Pair Postulate?
The linear pair postulate states that if two angles form a linear pair, then both angles are supplementary, and therefore have a sum of 180 degrees.
The proof that states that angle 1 and angle 3 are congruent angles is shown below:
Statement 1. ∠1 and ∠2 are a linear pair
Reason: Given
Statement 2: ∠1 and ∠2 are supplementary
Reason: Linear Pair Postulate
Statement 3: m∠1 + m∠2 = 180°
Reason: Definition of Supplementary Angles
Statement 4: ∠2 = ∠4
Reason: Given
Statement 5: ∠3 = ∠4
Reason: Vertical Angles Theorem
Statement 6: ∠2 = ∠3
Reason: Corresponding angles theorem
Statement 7: m∠2 = m∠3
Reason: Corresponding angles are congruent
Statement 8: m∠1 + m∠3 = 180
Reason: Supplementary angle theorem
Statement 9: <1 and <3 are supplementary
Reason: Definition of supplementary angles
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