AIA Conjecture

Definition of AIA (Alternate Interior Angles) Conjecture

If two parallel lines are cut by a transversal, then the Alternate Interior Angles are congruent.

More about AIA Conjecture

Two pairs of alternate interior angles are formed when two parallel lines are cut by a transversal.

Examples of AIA Conjecture

example of AIA Conjecture

Here a and b are two parallel lines and c is the transversal. ∠2, ∠7 and ∠3, ∠6 are pairs of alternate interior angles. According to AIA (alternate interior angle) conjecture ∠2 and ∠7 are congruent, and ∠3 and ∠6 are congruent and can be represented as ∠2 ∠7 and ∠3 ∠6.


Video Examples: Interior Angle Sum Conjecture Video #1


Solved Example on AIA Conjecture

Ques: The lines l and m are parallel in the figure. Which of the angles satisfies the AIA conjecture?

example of AIA Conjecture

Choices:
  • A. ∠5 and ∠6
  • B. ∠1 and ∠6
  • C. ∠3 and ∠8
  • D. ∠1 and ∠4

Correct Answer: C

Solution:

  • Step 1: Only alternate interior angles of parallel lines satisfy the AIA conjecture.
  • Step 2: Angles formed inside of the two parallel lines and on the opposite of the transversal are called alternate interior angles of the parallel lines.
  • Step 3: The alternate interior angles of the figure are ∠3 and ∠8, ∠4 and ∠5.
  • Step 4: So, ∠3 and ∠8 satisfies the AIA conjecture.

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