Understanding Alternate Interior Angles | Definition, Properties, and Applications in Geometry

alternate interior angles

Alternate interior angles are a pair of interior angles that are formed when two lines are intersected by a third line, also known as a transversal

Alternate interior angles are a pair of interior angles that are formed when two lines are intersected by a third line, also known as a transversal. These angles are located on opposite sides of the transversal and on the inside of the two intersected lines.

In the diagram below, assume that line l and line m are two parallel lines intersected by a transversal line t:

“`
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________|________
| | |
| | |
| | |
| l | m |
| | |
| | |
|_______|_______|
|
“`

Inside this diagram, there are two pairs of alternate interior angles:

1. Angle 1 and Angle 5: Both of these angles are located between the parallel lines l and m, and on opposite sides of the transversal t.
2. Angle 2 and Angle 6: Similarly, both of these angles are inside the parallel lines l and m but on opposite sides of the transversal.

The key property of alternate interior angles is that they are congruent (have the same measure) if the two intersected lines are parallel. This means Angle 1 is congruent to Angle 5, and Angle 2 is congruent to Angle 6.

Alternate interior angles are important in many geometrical proofs and applications, especially when working with parallel lines and transversals.

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