Alternate Interior Angles

Definition: If two lines are intersected by a transversal (third line):
Alternate interior angles are located inside the pair of lines and on opposite sides of the transversal. When the two lines crossed by a transversal are parallel, the alternate interior angles are equal.

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Example: Identify a pair of alternate interior angles

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Solution: 

Use the definition to identify pairs of alternate interior angles.

Step 1: We know alternate interior angles are located “inside” a pair of lines. In this figure, the pair of lines is Line l and Line m. Keeping this in mind, we can narrow our angles down to angles ∠3, ∠4, ∠5 and ∠6, because they are all on the inside or interior or our pair of lines, l and m.

Step 2: The definition also tells us that alternate interior angles are located on opposite sides of the transversal (intersecting line), which here is Line t. Looking again at our interior angles, ∠3 , ∠4, ∠5 and ∠6, we can form two pairs of angles that fit this description of being on opposite sides of the transversal.

Step 3: Based on this definition of alternate interior angles, we can identify two pairs from the figure:

∠3 and ∠6 are alternate interior angles because they are on opposite sides of the transversal, and are inside the pair of lines.
∠4 and ∠5 are alternate interior angles because they are on opposite sides of the transversal, and are inside the pair of lines.

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