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
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?
- A. ∠5 and ∠6
- B. ∠1 and ∠6
- C. ∠3 and ∠8
- D. ∠1 and ∠4
Correct Answer: C
- 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.