alternate interior angles theorem
The alternate interior angles theorem states that if two parallel lines are intersected by a transversal (a line that crosses both of the parallel lines), then the pairs of alternate interior angles are congruent
The alternate interior angles theorem states that if two parallel lines are intersected by a transversal (a line that crosses both of the parallel lines), then the pairs of alternate interior angles are congruent.
In other words, if line l and m are parallel lines, and line t intersects l and m as shown below:
a———b
/ \
t /_____________\
c d
Then the angles a and d, as well as angles b and c, are alternate interior angles. The theorem states that if l || m, then angle a is congruent to angle d, and angle b is congruent to angle c.
In mathematical notation:
If l || m and t is a transversal, then
angle a ≅ angle d
angle b ≅ angle c
This theorem is useful in proving properties of geometric figures, especially when dealing with parallel lines and angles formed by transversals.
More Answers:
Understanding the Consecutive Interior Angles Theorem | Exploring Angle Relationships in Geometry with Parallel Lines and TransversalsUnderstanding the Corresponding Angles Theorem | Exploring the Relationship Between Angles when Parallel Lines are Intersected by a Transversal
Exploring the Properties and Applications of Alternate Exterior Angles in Geometry