13 - Motion Geometry II

Abstract

This chapter discusses motion geometry for the definition of parallel lines. When lines are slide images of one another, the lines are called parallel lines. When no slide works, the lines are not parallel. When a pair of parallel lines is cut by a third line, it is a transversal. Any line that crosses two other lines, not necessarily parallel, is called a transversal. When two lines are cut by a transversal, a pair of angles in like positions with respect to the transversal are called corresponding angles. When the lines are parallel, corresponding angles are slide-congruent under a suitable slide along the transversal. The chapter illustrates alternate interior angles, alternate exterior angles, and perpendicularity. It presents a classification of triangles and quadrilaterals in terms of the numbers and kinds of symmetries. A quadrilateral is a four-sided figure. The chapter classifies quadrilaterals into eight types, according to their symmetries.