AEA Conjecture

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

example 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

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

example of AEA Conjecture

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

Correct Answer: B

Solution:

  • 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.

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