alternate interior angles
Alternate interior angles are a pair of angles that lie on opposite sides of a transversal and inside a pair of lines
Alternate interior angles are a pair of angles that lie on opposite sides of a transversal and inside a pair of lines. These angles are formed when a transversal intersects two parallel lines.
To identify alternate interior angles, imagine two parallel lines intersected by a transversal line. The angles on the inside of the parallel lines and on opposite sides of the transversal are alternate interior angles. They are called “alternate” because they are located on alternate sides of the transversal, and “interior” because they are inside the two parallel lines.
When two parallel lines are intersected by a transversal, alternate interior angles are congruent. In other words, their measures are equal. This property is called the Alternate Interior Angles Theorem.
The theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. Mathematically, it can be represented as:
If line a || line b, and transversal line t intersects lines a and b, then the alternate interior angles formed, ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8, are congruent.
This theorem is useful in various geometric proofs and can be applied to solve problems involving angles formed by intersecting lines in a parallel line configuration.
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