Parallel Lines

Parallel Illusion
Parallels and Transversals

Parallel and Transversal Parallel lines are lines in a plane that do not intersect even when extended. A third line that crosses parallels is called a transversal. This divides the plane into three areas - above and below the parallels [exterior] and between them [interior.]
Parallel and Transversal

Transversals and Angles

Transversal and Angles A transversal crossing parallel lines creates 8 angles which have "pair" names: alternate interior angles - ∠4, ∠6 and ∠3, ∠5;
alternate exterior angles - ∠1, ∠7 and ∠2, ∠8;
corresponding angles - ∠1, ∠5 and ∠2, ∠6 and ∠3, ∠7 and ∠4, ∠8.
ALTERNATE INTERIORS ARE EQUAL;
ALTERNATE EXTERIORS ARE EQUAL;
CORRESPONDING ANGLES ARE EQUAL
Transversal and Equal Angle Pairs

Other Parallelisms

Step Ladder LINES PARALLEL TO A THIRD LINE ARE PARALLEL;
LINES PERPENDICULAR TO A THIRD LINE ARE PARALLEL.
In a step ladder, each step is parallel to the step immediately below it and the bottom step is parallel to the floor. Yardlines on a football field are parallel and perpendicular to the sidelines.
Football Field

The Parallel Postulate

Parallel Postulate Euclid correctly postulated [meaning it cannot be proved] that only one line can pass through a point and be parallel to a given line. Contrary assumptions lead to alternate valid and consistent geometries.
Euclidean Geometry Elliptic Geometry Hyperbolic Geometry

Self Quiz

1. Name the angle pair.
Corresponding Angles
2. True or False? Equal Alternate Interior Angles
3. What geometry is suggested by the surface of a potato chip?

Potato Chips

Answers

1. corresponding angles
2. true
3. hyperbolic

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