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.

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.

Solved Example on AEA Conjecture

The lines l and m are parallel in the figure. Which of the angles satisfies the 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.

Related Terms for AEA Conjecture

• Alternate Exterior Angles
• Alternate Interior Angles
• Angle
• Congruent
• Conjecture
• Parallel Lines
• Transversal

Additional Links for AEA Conjecture

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• Back to Mathematics Dictionary

• Alternate Exterior Angles
• Alternate Interior Angles
• Angle
• Congruent
• Conjecture
• Parallel Lines
• Transversal