Alternate Exterior Angles Theorem
“If two lines are parallel and intersected by a transversal, then the alternate exterior angles are considered congruent angles or angles of equal measure,” according to the alternate exterior angle theorem.
In other words, alternate exterior angles are congruent with each other. Using the same figure as before, we can see that ∠1 & ∠8 and ∠2 & ∠7 are pairs of opposite exterior angles. Let’s look at how they’re congruent (equal).
Given: AB and CD parallel lines on a transversal Y.
[Hint: The following axioms will be used to establish the above theorem:
When two lines are parallel, the corresponding angles are congruent, according to the Corresponding Angle Axiom.
When the corresponding angles created by two lines are congruent, the lines are parallel.]
To Prove: ∠1 = ∠8
Proof: To demonstrate this conclusion, consider the vertically opposite angle of 1.
In this case, the vertically opposite angle of ∠1 is ∠4.
As a result, ∠1 = ∠4 (vertically opposed angles).
In this case, line AB || CD,
∠4 = ∠8 (which corresponding angles axiom)
∠1 = ∠8 (transitivity)
As a result, ∠1 = ∠8 proved.
Alternate Exterior Angles
Alternate Exterior Angles in maths are generated when a transversal connects two or more parallel lines at different locations. Alternate exterior angles are a pair of angles that lie on the opposite sides of a transversal line and on the outer sides of two intersecting lines. When a transversal line intersects two other lines, it creates several pairs of angles, and alternate exterior angles are one of these pairs. You can also check the article on parallel lines and traversal to study it in detail.
The phrase exterior refers to something that is located on the outside. They are placed on opposing sides of the transversal and lie outside the two crossed lines. As a result, the two external angles formed at the opposite ends of the transversal in the outside component are termed a pair of alternative exterior angles and are always equal. When a transversal intersects two parallel lines, we obtain two such pairs of alternate exterior angles.
In this article, you will study what are alternate exterior angles, the alternate exterior angles theorem, and examples of alternate exterior angles.
Table of Content
- Alternate Angles in Geometry
- Alternate Exterior Angles in Geometry
- Alternate Exterior Angles Theorem
- Converse of Alternate Exterior Angles Theorem
- Are Alternate Exterior Angles Congruent?
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