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Lines and Angles

Lines and angles are two of the most basic elements of geometry.

What is a line?

A line is an abstract concept. It has no width, only length, and that length is infinite in both directions. A part of a line that is bounded by two points is called a line segment. 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?

The segment addition postulate states that if we have a line segment defined by two points, A and C, a third point , B, is on the same line if (and only if) the length of segment AB plus the length of segment BC is equal to the length of AC:

segment addition postulate

|AB|+|BC|=|AC|

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°.

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Now that we've briefly explained the basic concept of lines and angles in geometry, let's scroll down to the post below that explains these concepts more in depth. For specific geometry problems in the area of lines and angles, check out the following links:
Intersecting Lines and Angles
Parallel Lines
Perpendicular Lines

l1 and l2 are equidistant

Parallel Lines are Equidistant

Consecutive Interior Angles Theorem in Geometry

Consecutive Interior Angles Converse Theorem

3 parallel lines theorem

Three Parallel Lines Theorem

Angle Bisector with 2 distances

Converse of the Angle Bisector Equidistant Theorem

Angle Bisector with 2 distances

Angle Bisector Equidistant Theorem

intercept theorem

Intercept Theorem

2 lines parallel to a third line

Two Lines Parallel to a Third are Parallel to Each Other

two parallel line segments

Converse Alternate Interior Angles Theorem

shortest distance theorem

Shortest Distance Theorem

What is a line in geometry?

Lines and Angles in Geometry

Two right angles in geometry

Linear Pair Perpendicular Theorem

Proving that lines are parallel in geometry

Converse of the Corresponding Angles Theorem

Alternate Interior Angles Theorem in Geometry

Alternate Interior Angles Theorem

Consecutive Interior Angles Theorem in Geometry

Consecutive Interior Angles Theorem

Intersecting lines in geometry

Vertical Angles Theorem

Line perpendicular to 2 parallel lines in geometry

Perpendicular Transversal Theorem

Line perpendicular to 2 parallel lines in geometry

Converse Perpendicular Transversal Theorem

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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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