Concept

Alternate Interior Angles

Consider a pair of lines cut by a transversal. The pairs of interior angles with different vertices that lie on opposite sides of the transversal are called alternate interior angles.

In the diagram, two pairs of angles can be identified as alternate interior angles.

Pair 1 : Pair 2 : ∠ 3 and ∠ 5 ∠ 4 and ∠ 6

If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. The same logic in reverse can be applied. If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.

If	Then
$ℓ_{1} ∥ ℓ_{2}$	$∠ 3 ≅ ∠ 5$ and $∠ 4 ≅ ∠ 6$
$∠ 3 ≅ ∠ 5$ or $∠ 4 ≅ ∠ 6$	$ℓ_{1} ∥ ℓ_{2}$

These statements are supported by the Alternate Interior Angles Theorem and its converse.

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Concept

Alternate Interior Angles

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