Geometry

• Basic concept and terms in geometry

  • Point
  • Line
  • Plane
• Geometric terms

  • collinear points
  • coplaner points
  • coplanar lines
  • line segment
  • ray
  • parallel lines
  • skew lines
• Point:

  • An exact location with no dimension
  • Named using a capital letter in space
• Line:

  • A set of points arranged in a row
  • Extended endlessly in both directions
  • One-dimensional figure
  • Two points determine a line
  • Named using a lowercase letter or any two points on the line
• Plane:

  • A set of points in an endless flat surface
  • Determined by:
  • Three non-collinear points
  • Two intersecting lines
  • Two parallel lines
  • A line and a point not on the line
  • Named using a lowercase letter or three points on the plane
• Geometric Terms:

  • Collinear points are points on the same line
  • Coplanar points are points on the same plane
  • Coplanar lines are lines on the same plane
• Line Segment:

  • Part of a line with two endpoints
  • Named as line segment AB or segment AB
• Ray:

  • Subset of a line with only one endpoint
  • Extended endlessly in one direction
  • Named as ray AB
• Parallel Lines:

  • Coplanar lines that do not intersect
• Skew Lines:

  • Lines that do not lie on the same plane
• Perpendicular Lines:

  • Two intersecting lines that form right angles
• Types of angles:

  • Acute angle: measures greater than 0 but less than 90°
  • Right angle: measures exactly 90°
  • Obtuse angle: measures greater than 90° but less than 180°
• Additional types of angles:

  • Zero angle: measures 0°
  • Straight angle: measures 180°
  • Reflex angle: measures greater than 180° but less than 360°
  • Perigon: measures 360°
• Angle Pairs:

  • Two angles are adjacent if they are coplanar, have a common vertex and common side but no common interior points
  • Two angles are complementary if the sum of their measures is 90°
  • Two angles are supplementary if the sum of their measures is 180°
  • Two angles form a linear pair if they are both adjacent and supplementary
  • Vertical angles are a pair of non-adjacent angles when two lines intersect
  • Vertical angles are congruent
• Postulates are statements accepted to be true without proof
• Line postulate -There exists exactly one line passing through two distinct points
• Plane postulate -There exists exactly one plane that contains three distinct points
• Line intersection postulate -The intersection of two distinct lines is exactly one point
• Plane intersection postulate -The intersection of two distinct planes is exactly one line
• Segment Addition Postulate: AB + BC = AC
• Angle Addition Postulate: In triangle PQR, the sum of angles PQS and SQR equals angle POR
• Linear Pair Postulate: If two angles form a linear pair, then their supplementary angles are congruent
• Vertical Angle Theorem: A pair of vertical angles are congruent
• Theorems are statements that can be demonstrated and be proven true using definitions, postulates, mathematical arguments, and even other theorems.
• Mathematical system A system made up of undefined terms, defined terma, axioms/postulates, and theorems that are used in proving logical conclusions in geometry.
• Undefined terms These are the terms that cannot be defined but they have their characteristics & can be described.
• Defined terms - These are the terms that have definition.
• Non- Collinear points are points that do not lie on one straight line

  A, B and C are non collinear points
• Non- Coplanar points - are points that do not lie on one plane X, Y and V are non coplanar points
•  polygon is a closed and flat shape made of straight lines. Polygons have at least three sides and three angles. A polygon cannot have any curved sides.
•  concave polygon - is a polygon which is not convex. This polygon is just the opposite of a convex polygon. A simple polygon is considered as a concave polygon if and only if at least one of the interior angles is a reflex angle (between 180° and 360°). It is also called a non-convex polygon
• Convex Polygon – A polygon is said to be convex if all the interior angles of the polygon are less than 180 degree. This means that all the vertices of the polygon will point outwards, away from the interior of the shape.