• Study Resource
  • Explore
    • 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
Lecture notes
Lecture notes

... Proposition 14. If two angles have a side in common, and if the noncommon sides are on different sides of the common side, and if the angles are together equal to two right angles, then the noncommon sides lie along the same straight line. This is a converse of Proposition 13. The reasoning is simil ...
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay

2014 – First Place – Anna Riffe - SIGMAA – History of Mathematics
2014 – First Place – Anna Riffe - SIGMAA – History of Mathematics

Justifications So Far
Justifications So Far

Chapter 2: Reasoning and Proof
Chapter 2: Reasoning and Proof

S1 Lines, angles and polygons
S1 Lines, angles and polygons

UNIT 5
UNIT 5

Final - Han
Final - Han

SD School Geometry
SD School Geometry

Since P is the centroid of the triangle ACE
Since P is the centroid of the triangle ACE

S1 Lines, angles and polygons
S1 Lines, angles and polygons

Exploring Angle Pairs
Exploring Angle Pairs

Exploring Angle Pairs
Exploring Angle Pairs

Swampscott Public Schools Core Standards/Curriculum
Swampscott Public Schools Core Standards/Curriculum

Similarity, Congruence and Proofs - 3
Similarity, Congruence and Proofs - 3

1. Refer to the figure on page 240. 2. Refer to the figure on page 240
1. Refer to the figure on page 240. 2. Refer to the figure on page 240

Origami building blocks: Generic and special four
Origami building blocks: Generic and special four

MATHEMATICS Algebra, geometry, combinatorics
MATHEMATICS Algebra, geometry, combinatorics

Notetaking Guide
Notetaking Guide

Triangle Congruence LAB
Triangle Congruence LAB

SMART Notebook
SMART Notebook

problem solving - A Learning Place A Teaching Place
problem solving - A Learning Place A Teaching Place

4. Shape, Dimension, and Geometric Relationships
4. Shape, Dimension, and Geometric Relationships

PARALLELOGRAMS AND RECTANGLES
PARALLELOGRAMS AND RECTANGLES

Geometry Triangle Congruence Criteria Unit CO.8 OBJECTIVE #: G
Geometry Triangle Congruence Criteria Unit CO.8 OBJECTIVE #: G

< 1 ... 20 21 22 23 24 25 26 27 28 ... 604 >

Line (geometry)



The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth. Lines are an idealization of such objects. Until the seventeenth century, lines were defined in this manner: ""The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points""Euclid described a line as ""breadthless length"" which ""lies equally with respect to the points on itself""; he introduced several postulates as basic unprovable properties from which he constructed the geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of nineteenth century (such as non-Euclidean, projective and affine geometry).In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it.When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object). The properties of lines are then determined by the axioms which refer to them. One advantage to this approach is the flexibility it gives to users of the geometry. Thus in differential geometry a line may be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and, for example, permits physicists to think of the path of a light ray as being a line.A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew, but unlike lines they may be none of these, if they are coplanar and either do not intersect or are collinear.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report