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.]
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
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.
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.
1. Name the angle pair.
2. True or False?
3. What geometry is suggested by the surface of a potato chip?
1. corresponding angles