Understanding Alternate Exterior Angles | Properties, Congruence, and Applications

Alternate Exterior Angles

Alternate exterior angles are pairs of angles that are formed when two parallel lines are intersected by a transversal

Alternate exterior angles are pairs of angles that are formed when two parallel lines are intersected by a transversal. A transversal is a line that crosses two other lines.

When two parallel lines are intersected by a transversal, the alternate exterior angles are located on the opposite side of the transversal and on the outer edges of the parallel lines. In other words, these angles are located outside the parallel lines and on opposite sides of the transversal.

Alternate exterior angles have a unique relationship: they are congruent, meaning that they have the same measure. This property holds true for all pairs of alternate exterior angles formed by parallel lines and a transversal.

To better understand alternate exterior angles, consider the following diagram:

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A ——- B
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C ——- D
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In the diagram, lines AB and CD are parallel, while line AC is a transversal that intersects the parallel lines. The alternate exterior angles are angle 1 and angle 8, as well as angle 2 and angle 7. These angles are congruent, meaning that angle 1 is equal in measure to angle 8, and angle 2 is equal in measure to angle 7.

Knowing the properties of alternate exterior angles can be helpful in solving problems involving parallel lines and transversals. For example, if you have two parallel lines and are given the measure of one alternate exterior angle, you can determine the measure of its corresponding angle using the congruence property.

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