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.
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