Alternate Exterior Angles
Alternate exterior angles are a pair of angles that are on opposite sides of a transversal and are located outside the two intersecting lines
Alternate exterior angles are a pair of angles that are on opposite sides of a transversal and are located outside the two intersecting lines. When two parallel lines are intersected by a transversal, alternate exterior angles are congruent. Let’s take a closer look at the concept of alternate exterior angles.
Consider two parallel lines, L₁ and L₂, that are intersected by a transversal line, T. There are four pairs of alternate exterior angles formed in this scenario. Let’s label them Angle 1, Angle 2, Angle 3, and Angle 4 as shown below:
_________
| |
1 | | 2
| |
|_________|
3 4
Angle 1 and Angle 2 are alternate exterior angles, as they lie on opposite sides of the transversal T, and they are located outside the lines L₁ and L₂. Similarly, Angle 3 and Angle 4 are alternate exterior angles.
The key property of alternate exterior angles is that they are congruent when the lines L₁ and L₂ are parallel. In other words:
Angle 1 ≅ Angle 2
Angle 3 ≅ Angle 4
This congruence property holds true for any pairs of alternate exterior angles formed by parallel lines and a transversal.
Alternate exterior angles are helpful in solving various types of problems involving angles formed by parallel lines and a transversal. For instance, they can be used to find the measures of unknown angles by using the congruence property. Additionally, alternate exterior angles can be used to prove that two lines are parallel if their alternate exterior angles are congruent.
Overall, alternate exterior angles play a crucial role in understanding the relationships between angles formed by parallel lines and a transversal.
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