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Answer :
When parallel lines are cut by a transversal, several properties and relationships are formed.
Here's a clear and concise description:
1. Corresponding angles: Corresponding angles are congruent. They are formed when a transversal intersects two parallel lines, and they are in the same relative position on each line. For example, if angle 1 and angle 5 are corresponding angles, then angle 1 is congruent to angle 5.
2. Alternate interior angles: Alternate interior angles are congruent. They are formed when a transversal intersects two parallel lines, and they are on opposite sides of the transversal and inside the parallel lines. For example, if angle 3 and angle 6 are alternate interior angles, then angle 3 is congruent to angle 6.
3. Alternate exterior angles: Alternate exterior angles are congruent. They are formed when a transversal intersects two parallel lines, and they are on opposite sides of the transversal and outside the parallel lines. For example, if angle 2 and angle 7 are alternate exterior angles, then angle 2 is congruent to angle 7.
4. Same-side interior angles: Same-side interior angles are supplementary. They are formed when a transversal intersects two parallel lines, and they are on the same side of the transversal and inside the parallel lines. For example, if angle 3 and angle 5 are same-side interior angles, then angle 3 + angle 5 = 180 degrees.
These properties and relationships help us analyze and solve problems involving parallel lines cut by a transversal, allowing us to find missing angles or prove other geometric properties. Understanding these concepts is essential in geometry.
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