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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Parallel lines are lines in a plane that are the same distance apart and do not cross
Parallel lines can be horizontal, vertical, or diagonal within a plane
Parallel lines must exist in the same plane to be considered parallel
A transversal is a line that intersects at least two other lines
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 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 are equal and formed when two lines intersect
Parallel lines can be represented by linear equations in the slope-intercept form
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
The slope of a line can be calculated using the formula m=(y2-y1)/(x2-x1)
The properties of parallel lines and transversals can be used to solve problems involving unknown angles
The slopes of two lines can be compared to confirm parallelism
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Orientation of parallel lines
Parallel lines can be horizontal, vertical, or diagonal but always equidistant.
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Coplanar requirement for parallelism
Lines must be in the same plane to be parallel; known as coplanar.
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A ______ crosses at least two other lines and can create unique angles when intersecting with parallel lines.
transversal
