Presentation Notes
Presentation Notes

... In this theorem, the conclusion is that the square of the hypotenuse is equal to the sum of the other two sides. A theorem can also be represented in the form: If p then q, where p is the Hypothesis and q is the Conclusion In symbols this is written as p ⟹ q , and read as ‘p implies q’, or ‘if p the ...
Course Overview
Course Overview

Task - Illustrative Mathematics
Task - Illustrative Mathematics

Example #2
Example #2

Course Notes - Mathematics
Course Notes - Mathematics

Jeapordy - Chapter 9
Jeapordy - Chapter 9

Geometry - Chapter 03 Summary
Geometry - Chapter 03 Summary

Geometry Curriculum - Oneonta City School District
Geometry Curriculum - Oneonta City School District

5. PAIR OF STRAIGHT LINES
5. PAIR OF STRAIGHT LINES

Geometry Curriculum Guide
Geometry Curriculum Guide

Geometry Experiment with transformations in the plane Understand
Geometry Experiment with transformations in the plane Understand

Geometry Semester Test Review CHAPTER 1 1.2 Points Lines and
Geometry Semester Test Review CHAPTER 1 1.2 Points Lines and

... y  8x  1 that contains (6, 2) 35) Write an equation of the line perpendicular ...
Undefined Terms: Points, Lines, and Planes Collinear vs
Undefined Terms: Points, Lines, and Planes Collinear vs

... Things to Remember About Rhombi Constructing a Rhombus What is the Difference Between a Rhombus and a Square? Draw and Label a Trapezoid Things to Remember About Trapezoids Constructing the Median of a Trapezoid Relationships Between Quadrilaterals ...
Sec 3.7 Equations of Lines in the Coordinate Plane
Sec 3.7 Equations of Lines in the Coordinate Plane

Coordinate Geometry
Coordinate Geometry

Geometry Proofs
Geometry Proofs

Any three points lie on a straight line or a circle
Any three points lie on a straight line or a circle

Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in
Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in

... Then pABE and pBEF are alternate interior angles, as are pCBE and pDEB. pABG and pFEH are alternate exterior angles, as are pCBG and pDEH. pGBC and pBEF are a pair of corresponding angles, as are pGBA & pBED, pCBE & pFEH, and pABE & pDEH. pCBE and pFEB are interior angles on the same side of the tra ...
GEOMETRICAL EXTREMA SUGGESTED BY A LEMMA OF
GEOMETRICAL EXTREMA SUGGESTED BY A LEMMA OF

Geometry Unit Plan - Orange Public Schools
Geometry Unit Plan - Orange Public Schools

Definitions of Key Geometric Terms
Definitions of Key Geometric Terms

Priority Standards Checklist Priority Standard Geometry PRIORITY
Priority Standards Checklist Priority Standard Geometry PRIORITY

Slide 1
Slide 1

Co-incidence Problems and Methods
Co-incidence Problems and Methods

Name_________________________ Due on: :___ Geometry 2nd
Name_________________________ Due on: :___ Geometry 2nd

Duality (projective geometry)

In geometry a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language (§ Principle of Duality) and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a duality. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry.