MATH 202 Chapter Notes - Chapter 14: Bisection
Document Summary
Reflections, translations, and rotations are the fundamental distance-preserving transformations of the plane. A shape or design has translation symmetry if there is a translation such that the shape or design as a whole occupies the same place in the plane both before and after translation. With a straightedge and a compass, we can construct the perpendicular bisector of a given line segment, and we can bisect a given angle. Both of these constructions produce an associated rhombus. The constructions give the desired results because of special properties of rhombuses: the diagonals in a rhombus are perpendicular and bisect each other, and the diagonals in a rhombus bisect the angles in the rhombus. We call 2 shapes or objects similar if all distances between corresponding parts of the shapes or objects are scaled by the same factor called a scale factor. We related both methods to setting up and solving a proportion.
