Based on the converse of corresponding angles theorem, the statements and reasons that prove that p║q are given below.
What is the Converse of Corresponding Angles Theorem?
The converse of corresponding angles theorem states that, if two corresponding angles that are formed by a transversal and two lines are congruent, then the two lines are parallel lines.
Using the converse of corresponding angles theorem, we can prove that p║q with the following statements and reasons:
Statement 1: ∠1 ≅ ∠2
Reason 1: given
Statement 2: ∠1 and ∠3 are vertical angles
Reason 2: Def. of vertical angles
Statement 3: ∠1 ≅ ∠3
Reason 3: Vertical angles theorem
Statement 4: ∠3 ≅ ∠2
Reason 4: Transitive property
Statement 5: P || q
Reason 5: Converse of corresponding angles theorem
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