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Explore the fundamentals of parallel lines in geometry, including their definition, properties, and the role of transversals in forming angles. Understand how corresponding, alternate, and consecutive angles are classified and used to solve geometric problems. Learn how to represent parallel lines in coordinate geometry using linear equations and determine their slope to confirm parallelism.

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## Definition of Parallel Lines

### Equidistance and Non-Intersecting

Parallel lines are lines in a plane that are the same distance apart and do not cross

### Orientation

Parallel lines can be horizontal, vertical, or diagonal within a plane

### Coplanarity

Parallel lines must exist in the same plane to be considered parallel

## Transversals and Angles

### Definition of Transversal

A transversal is a line that intersects at least two other lines

### Types of Angles Formed

Corresponding Angles

Corresponding angles are congruent and located on the same side of the transversal in relation to the parallel lines

Alternate Interior Angles

Alternate interior angles are congruent and located on opposite sides of the transversal within the parallel lines

Alternate Exterior Angles

Alternate exterior angles are congruent and located on opposite sides of the transversal outside the parallel lines

### Consecutive Angles

Consecutive Interior Angles

Consecutive interior angles are supplementary and located on the same side of the transversal within the parallel lines

Consecutive Exterior Angles

Consecutive exterior angles are supplementary and located on the same side of the transversal outside the parallel lines

### Vertically Opposite Angles

Vertically opposite angles are equal and formed when two lines intersect

## Coordinate Geometry and Parallel Lines

### Representation of Parallel Lines

Parallel lines can be represented by linear equations in the slope-intercept form

### Conditions for Parallel Lines

Identical Slopes

For two lines to be parallel, they must have the same slope

Different Y-Intercepts

Parallel lines have different y-intercepts, indicating they cross the y-axis at different points

### Calculation of Slope

The slope of a line can be calculated using the formula m=(y2-y1)/(x2-x1)

## Applications of Parallel Lines

### Problem Solving

The properties of parallel lines and transversals can be used to solve problems involving unknown angles

### Validation of Parallelism

The slopes of two lines can be compared to confirm parallelism

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