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Home » Lines and Angles » Lines and Angles

Lines and Angles

Last updated: May 1, 2024 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

In today's lesson, we'll discuss the concepts of lines and angles in geometry, including line segments, line axioms, and how two intersecting lines form an angle.

What is a line?

A line is an abstract concept. It has no width, only length, and that length is infinite in both directions. One of the formal definitions of a line is that it is the collection of all points that are the same distance from two other points on a plane:

What is a line?

Each one of the points C, D, E, F, G and H is the same distance from A and B. If we drew all the possible points that are like this, we’d have the line drawn above.

Line segments

A straight line extends infinitely in both directions. But we often deal with a specific part of the line, defined by two points on the line. Such parts are called line segments, and are defined by the two points. For example, in drawing above we have a line segment between points G and H, called GH, another segment between D and (DG) and so on.

Line axioms

In Euclidean geometry (which is the kind of geometry we use here), it is an axiom that you can draw a line between any two points. An axiom is something taken as a basic rule which is self-evident, it does not have a proof.

Another axiom is that for every straight line and every point not on that line, there is one straight line that passes through that point, and never intersects the first line. Such lines are called Parallel lines, which we will deal with in a subsequent section.

Angles

When 2 lines or line segments intersect, they form angles:

This is an angle

We measure angles in units called degrees, and marked with a °, where a full circle is 360°. Why 360? It is just a very convenient number, because it is divisible by many other numbers – 2,3,4,5,6,9, 10, 12….

« Linear Pair Perpendicular Theorem
What are Polygons? »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected].

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About

Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

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