Alternate interior
angles that are on opposite sides of the transversal and in between the parallel lines
Alternate Interior Angles are pairs of angles that are formed when a transversal intersects two parallel lines. They are called alternate because they are on opposite sides of the transversal and interior because they are inside the two parallel lines.
In other words, if we have two parallel lines and a transversal line intersects them, the angles that are formed on the inside of the parallel lines and on opposite sides of the transversal are called alternate interior angles.
The important thing to note about alternate interior angles is that they are congruent, which means they have the same size and measure. This congruence property is a consequence of the fact that the two parallel lines create a set of congruent angles when intersected by the transversal.
The mathematical notation for alternate interior angles is ∠1 and ∠3, ∠2 and ∠4 in the figure below:
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_______ _______
| | | |
| | | |
_____| 1 |_____| 2 |
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|________| |________|
∠3 ∠4
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It’s important to understand the concept of alternate interior angles because it is used in many geometry proofs and theorems. For example, one theorem states that when a transversal intersects two parallel lines, the alternate interior angles are congruent.
More Answers:
The Corresponding Angles Postulate: Key Concepts In GeometrySame-Side Interior Angles And Their Special Relationship.
Mastering Geometry: Congruent Alternate Exterior Angles In Parallel Lines And Transversals