Understanding Corresponding Angles
Corresponding angles are formed when a transversal intersects two parallel lines. They occupy the same relative position at each intersection.
- Examples:
- If line A and line B are parallel, and line C is the transversal, then angle 1 on line A and angle 2 on line B are corresponding angles.
- Property:
- Corresponding angles are equal.

Exploring Alternate Interior Angles
Alternate interior angles are located on opposite sides of the transversal and inside the two parallel lines.
- Examples:
- In the previous setup, angle 3 and angle 4 are alternate interior angles.
- Property:
- Alternate interior angles are also equal when the lines are parallel.

Understanding Co-Interior Angles
Co-interior angles, also known as same-side interior angles, are found on the same side of the transversal and within the parallel lines.
- Examples:
- Continuing with the previous lines, angle 5 and angle 6 are co-interior angles.
- Property:
- The sum of co-interior angles is supplementary (i.e., they add up to 180 degrees).

Conclusion
These angle relationships are crucial in geometry, particularly in proofs and solving problems related to parallel lines. Understanding these concepts lays the foundation for further studies in geometry and mathematics.