question archive Consider two statements: (A) Two lines that are cut by a transversal are parallel (B) Alternate interior angle formed by these lines are congruent They are equivalent
Consider two statements: (A) Two lines that are cut by a transversal are parallel (B) Alternate interior angle formed by these lines are congruent They are equivalent
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Consider two statements: (A) Two lines that are cut by a transversal are parallel (B) Alternate interior angle formed by these lines are congruent They are equivalent. See below for explanation.
Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Let's represent it in a form "if A then B": If two lines that are cut by a transversal are parallel [Part A] then alternate interior angles formed by these lines are congruent [Part B].
Converse theorem should look like "if B then A": If alternate interior angles formed by these lines are congruent [Part B] then two lines that are cut by a transversal are parallel [Part A].
So, these are two different theorems, each requiring its own proof. But, since both theorem ##A->B## and ##B->A## can be proven independently, both statement are equivalent. If one is true, another is as well, if one if false, another is well.
