Alternate Interior Angles
Nonadjacent interior that lie on opposite sides of a transversal. (3.1)
Alternate interior angles are pairs of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal. These angles are congruent, which means they have the same measure.
For example, suppose there are two parallel lines p and q, and a third line t is drawn intersecting p and q at points A and B respectively. If angle 1 and angle 2 are alternate interior angles, then angle 1 is congruent to angle 2. The same applies for angle 3 and angle 4, as shown in the diagram below:
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(Angle 1) (Angle 2)
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(Angle 3) \ / (Angle 4)
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X
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It is important to note that alternate interior angles are only congruent when the two intersecting lines are parallel. If the lines are not parallel, then the alternate interior angles will not have the same measure.
In conclusion, alternate interior angles are a pair of congruent angles that are formed by two parallel lines and a transversal. They are useful in geometry when finding missing angle measurements, and they obey certain rules that make them predictable and easy to work with.
More Answers:
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