Monday, November 13, 2006
Geometry (Class 26)
Overview
§4.7 (p.243) Triangles and Coordinate Proof
Review for Midterm
In 1637 the French mathematician Rene Descartes linked Algebra and Geometry by inventing the coordinate plane. This invention (or discovery depending on your viewpoint) opened the doors for the development of Analytic Geometry. Today we have an introduction to this “new” type of Geometry and begin to learn how we can use our algebraic skills to prove theorems about geometric shapes. (http://en.wikipedia.org/wiki/Ordinate)
Key Ideas
Use the coordinates to your advantage!
The main tools that can be used when writing coordinate proofs are the distance formula (to show two segments are of equal length and hence congruent), the midpoint formula (to find the location of the midpoint), the slope of a line (to show lines are parallel or perpendicular), and the Pythagorean Theorem (to show that a triangle is a right triangle).
In order to make the proof as easy as possible, place the figure wisely. For instance, place a vertex at the origin, or use the axes to form a right triangle, or use the symmetry of an isosceles triangle to your advantage by placing the base on the x-axis and the vertex angle on the y-axis.
Vocabulary
analytic geometry
coordinate proof
Assignment
§4.7 (Txt. p.247) #7-10, 22, 23, 35, 37, 38, 43
Chapter 4 Review (Txt. p.252) 5 most important problems--you pick them!
Permalink