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 Alternate Interior Angles     Angle     Congruent     Conjecture     Transversal  

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.

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.

Solved Example on AIA Conjecture

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

Related Terms for AIA Conjecture

• Alternate Interior Angles
• Angle
• Congruent
• Conjecture
• Transversal

Additional Links for AIA Conjecture

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