• Study Resource
  • Explore Categories
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Geometry
Geometry

fall final review
fall final review

Biconditionals and Definitions
Biconditionals and Definitions

review for the semester exam
review for the semester exam

Angle Relationships - Riverdale Middle School
Angle Relationships - Riverdale Middle School

High School Geometry
High School Geometry

Geometry Quarter 1 Review
Geometry Quarter 1 Review

SCDE Standards suggested for inclusion CCSSM Geometry SC
SCDE Standards suggested for inclusion CCSSM Geometry SC

Math 2 Lesson Plan - GSE ANALYTIC GEOMETRY
Math 2 Lesson Plan - GSE ANALYTIC GEOMETRY

Midterm Review Part 3
Midterm Review Part 3

Lines that intersect Circles
Lines that intersect Circles

Document
Document

if and only if - cloudfront.net
if and only if - cloudfront.net

AHSAA Homeschool Student Eligibility Exams Math
AHSAA Homeschool Student Eligibility Exams Math

Reteaching
Reteaching

... If a || b and b || c, then a || c. Lines a, b, and c can be in different planes. Theorem 3-9: If two lines are perpendicular to the same line, then those two lines are parallel to each other. This is only true if all the lines are in the same plane. If a ⊥ d and b ⊥ d, then a || b. Theorem 3-10: Per ...
1.5 Relations between Angles with a Common Vertex
1.5 Relations between Angles with a Common Vertex

0612ge
0612ge

3 - Wsfcs
3 - Wsfcs

Prove
Prove

Geo Spring Practice Exam 2015
Geo Spring Practice Exam 2015

Answers for the lesson “Prove Theorems about Perpendicular Lines”
Answers for the lesson “Prove Theorems about Perpendicular Lines”

Geometry 3.1
Geometry 3.1

problems
problems

... In 1733 there appeared the book Euclid Vindicated of All Flaw by the Jesuit priest Gerolamo Saccheri. In it the author purported to prove Euclid’s Fifth Postulate as a theorem. We now recognize basic flaws in his argument at certain crucial steps. However, the book was and is important in the develo ...
Chapter 2: Congruence
Chapter 2: Congruence

... Chapter 2 ...
22 The Existence of Parallel Lines
22 The Existence of Parallel Lines

< 1 ... 46 47 48 49 50 51 52 53 54 ... 134 >

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.
  • studyres.com © 2026
  • DMCA
  • Privacy
  • Terms
  • Report