Definition of AEA (Alternate Exterior Angle) Conjecture
AEA (Alternate Exterior Angle) Conjecture states that if two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
More About AEA Conjecture
Two pairs of alternate exterior angles are formed when two parallel lines are cut by a transversal
Examples of AEA Conjecture
Here a and b are two parallel lines and c is the transversal.∠2, ∠7 and ∠3, ∠6 are pairs of alternate exterior angles. According to AEA (alternate exterior 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: Alternate Exterior Angle Theorem
Solved Example on AEA Conjecture
The lines l and m are parallel in the figure. Which of the angles satisfies the AEA conjecture?
- A. ∠5 and ∠6
- B. ∠1 and ∠6
- C. ∠3 and ∠8
- D. ∠1 and ∠4
Correct Answer: B
- Step 1: Only alternate exterior angles of parallel lines satisfy the AEA conjecture.
- Step 2: Angles formed on the outside of two parallel lines and on the opposite of transversal are called alternate exterior angles of the parallel lines.
- Step 3: The alternate exterior angles of the figure are ∠1 and ∠6, ∠2 and ∠7.
- Step 4: Here, ∠1 and ∠6 are alternate exterior angles and hence congruent to each other.
- Step 5: So, ∠1 and ∠6 satisfy the AEA conjecture.