consecutive interior angles theorem
The Consecutive Interior Angles Theorem is a property in geometry that applies to parallel lines intersected by a transversal
The Consecutive Interior Angles Theorem is a property in geometry that applies to parallel lines intersected by a transversal. When two parallel lines are intersected by a transversal, consecutive interior angles are formed.
Consecutive interior angles are pairs of angles that lie on the same side of the transversal and are located between the two parallel lines. In other words, consecutive interior angles are a pair of angles that have a common vertex, one angle inside the two parallel lines, and the other angle outside of the two parallel lines.
The Consecutive Interior Angles Theorem states that when two parallel lines are intersected by a transversal, the consecutive interior angles are congruent. This means that the angles have the same measure.
Mathematically, if lines l and m are parallel, and line n is a transversal intersecting lines l and m, then the consecutive interior angles are congruent. This can be represented as:
∠1 ≅ ∠4
∠2 ≅ ∠3
In a diagram, these angles could be labeled as shown below:
l
|\
∠2 | \ ∠1
——–\——–
n \
——–/——–
∠3 | / ∠4
|/
m
The Consecutive Interior Angles Theorem is a useful tool in geometry to prove various angle relationships and solve problems involving parallel lines and transversals.
More Answers:
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