alternate exterior angles
Alternate exterior angles are a pair of angles formed when a transversal crosses two parallel lines
Alternate exterior angles are a pair of angles formed when a transversal crosses two parallel lines. They are located on opposite sides of the transversal and outside the two parallel lines.
To visualize alternate exterior angles, consider two parallel lines cut by a transversal. Let’s label the two parallel lines as line l and line m, and the transversal as line t. When line t intersects line l, it forms two pairs of alternate exterior angles. Similarly, when line t intersects line m, it also forms two pairs of alternate exterior angles.
The key property of alternate exterior angles is that they are congruent (equal) if the two lines being intersected by the transversal are parallel. In other words, if line l and line m are parallel, then the pairs of alternate exterior angles formed are congruent. This is known as the alternate exterior angles theorem.
The alternate exterior angles theorem can be stated as follows: If a transversal intersects two parallel lines, then the alternate exterior angles are congruent. Mathematically, if angle A and angle B are alternate exterior angles, and line l and line m are parallel, then angle A is congruent to angle B.
This theorem is useful in proving various geometric theorems and in solving problems that involve parallel lines and transversals. By identifying the pairs of alternate exterior angles and knowing that they are congruent, we can use this information to find missing angle measures and solve geometric puzzles.
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