Geometry

• Geometry


  The study of shapes and their measurements.
• Point


  Has a location but no shape or size, represented by a dot and named with a capital letter to name a point
• Line


  Can be labelled with a small letter or named using two points on the line
• Plane


  A flat surface that extends in all directions, has length and width
• Examples of plane


  • Plane N
  • Plane PAL
• Segment


  A subset of a line with two endpoints and definite length

  
• Ray


  A subset of a line with one endpoint and no definite length
• Line Postulate: For every pair of points, there is exactly one line that contains them
• Intersecting lines


  • Two lines with a common point
• Parallel lines


  • Coplanar lines that do not meet
• Coplanar


  Points or lines that lie on the same plane
• Noncoplanar


  Points or lines that do not lie on the same plane
• Collinear points


  Points that lie on the same line
• Noncollinear points


  Points that do not lie on the same line
• Angle


  Formed by two rays with the same endpoint (vertex), the rays are the sides
• Angle measurement


  Measured in degrees using a protractor
• Kinds of angles


  • Acute angle (>0° and <90°)
  • Right angle (90°)
  • Obtuse angle (>90° and <180°)
• The two greek words in geometry 


  "Geo" means "earth" and "metron" means "measure"
• Geometry


  The study of space, a branch of mathematics which deals with the sizes, shapes, positions, and properties of all things around us
• Geometry


  Comes from two Greek words: geo meaning earth and metri meaning measurement, therefore geometry means earth measurement
• Geometry was first developed by the ancient Greek philosopher Euclid


  Around 300 B.C.
• Euclid's first book, The Elements


  Has contributed greatly to the development of the study of Geometry
• Postulates


  Statements that are assumed to be true even without proof
• Theorems and corollaries


  Statements that need to be proven using postulates and definitions of terms
• Point


  Has no length, width or thickness, occupies no space
• Line


  Has infinite length but no width or thickness; is straight
• Plane


  Has infinite length and width but no thickness; is a flat surface
• Collinear points


  Points that lie on the same line
• Noncollinear points


  Points that do not lie on the same line
• Coplanar points and lines


  Points or lines that lie on the same plane
• Noncoplanar points and lines


  Points or lines that do not lie on the same plane
• Line Postulate


  For every pair of points, there is exactly one line that contains them
• Line Segment


  A subset of a line bounded by two points called endpoints
• Ray


  A subset of a line that has one endpoint and that extends infinitely in one direction
• Intersecting lines


  Two lines with a common point
• Parallel lines


  Coplanar lines that do not meet
• Angle


  A geometric figure formed by two rays (called sides) with a common endpoint called vertex
• Congruent angles


  Angles that have equal measures
• Adjacent angles


  Two coplanar angles that have a common vertex and a common side, and do not overlap
• Complementary angles


  Two angles whose sum of measures is 90 degrees