Alternate Exterior Angles
Alternate exterior angles are a pair of angles that are formed when a transversal intersects two lines
Alternate exterior angles are a pair of angles that are formed when a transversal intersects two lines. These angles are located on opposite sides of the transversal and outside the set of two lines.
To better understand alternate exterior angles, let’s consider the following diagram:
“`
Line 1
——————-
\ /
\ t /
\_________/
\ /
\ /
\ /
\/ Alternate
/\ Exterior
/ \
/ \
/ \
/ \
/ \ Line 2
“`
In the diagram, Line 1 and Line 2 are two parallel lines, and t is the transversal that intersects these lines. Here, alternate exterior angles are represented by the angles on opposite sides of the transversal, but outside the set of two lines.
In terms of angle relationships, alternate exterior angles are congruent. In other words, they have the same angle measure. This property can be expressed as:
∠1 ≅ ∠4
∠2 ≅ ∠3
This congruence occurs because alternate exterior angles are formed by creating a “Z” shape with the parallel lines and the transversal.
Besides their congruence, alternate exterior angles also have another important property. If the two parallel lines and the transversal are intersected by a third line, the sum of the alternate exterior angles will be equal to 180 degrees. This property is known as the Exterior Angle Theorem and can be expressed as:
∠1 + ∠2 = 180 degrees
This theorem holds true because the alternate exterior angles lie on a straight line when the third line intersects the parallel lines. Therefore, their sum will be equal to 180 degrees.
More Answers:
How to Calculate the Measure of Interior Angles in a Polygon: Formulas and ExamplesUnderstanding Alternate Interior Angles: Properties, Relationships, and Applications in Geometry
Understanding Exterior Angles in Polygons: The Exterior Angle Theorem Explained