The alternate interior angles theorem states that the alternate interior angles formed between parallel lines and a common transversal are congruent
The correct option that states the converse used to prove the given set of lines are parallel, l║n using the given angle pair ∠8 ≅ ∠19 is option C.
C) Alternate Interior Angles Converse
Reason:
The given congruent angles are ∠8 ≅ ∠19
Required:
To find the converse used to proof that lines l, and m are congruent
Solution:
The relationship between ∠8 and ∠19 = Alternate interior angles; Angles formed on the opposite side of a transversal on the interior area of the two intersected lines l and m
Given that angles ∠8 and ∠19 formed between lines l, and m by and the common transversal k are congruent, we have that by the converse of the alternate interior angles theorem which states where the alternate interior angles of two lines intersected by a common transversal are congruent, then the two lines are parallel, therefore, lines l, and n, are congruent
l║n
The correct option is therefore option C)
C) Alternate Interior Angles Converse
Learn more about Alternate Interior Angles theorem here:
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