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Geometry & spatial reasoning

Two or Three dimension figure

Geometry originates from Greek ge or gaia - meaning earth or land and metria meaning measuring, or measurement of earth or land.

Analytic geometry is the combination of geometry and algebra.

Geometry is the science of correct reasoning on incorrect figures. George Polya


Concepts & Generalizations


  • Relative position is used to locate objects in space (directions). Use vocabulary involving important prepositions-in, on, under, inside, between, upon, from, outside, above, and so on.
  • Spatial representations can be shown with models, diagrams, ... (geoboards, visual representation).
  • Spatial relationships and Geometric patterns can be found in our everyday world.


  • Area is the surface space of a two-dimenional space measured in square measurements.
  • Angle is made where two lines intersect.
  • Circle is a two dimensional closed figure with everypoint being equal distance from its center.
    • Circle properties include: circumference, diameter, radius, sector, chord, area, and infinite lines of symmetry
  • Congruence is when two figures have the same shape and size.
  • Coordinate system is a spatial reference system that uses vertical and horizontal references from a point of origin.
  • Line is
    • A line has different properties (line, line segments, ray)
  • Patterns can be described mathematically.
  • Parallel lines are lines in the same plane that do not intersect.
  • Perimeter is the distance around a shape measured in linear measurements.
  • Perpendicular lines intersect so they form a right angles or 90 degree angle. Can be made on a piece of paper holding the points on either end of the line together and folding at the mid point.
  • Pi is the relationship between the diameter of a circle and its circumference.
  • Plane is a flat surface such that if a straight line is draw from from on point on the line to another, the line would be entirely on the surface.
  • Point is a place in space that has a location, but no size. It is impossible to draw, because if it is, then it has size.
  • Polar coordinate system is a spatial reference system that uses and angle and distance for reference from a point of origin.
  • Polygon is a plane figure whose sides are line segments. They can be convex or non convex. Regular polygons have angles and sides all of equal measure.
  • Symmetry symmetric and asymmetric figures
    • Symmetry or line symmetry is an identical relationship on two sides of a line drawn through a figure or parts of a figure. A figure has line symmetry if a part can be flipped about a line so both parts coincides. A mirror can be used to illustrate symmetry if placing the mirror on the line of symmetry the reflection is the same as the figure in front of the mirror. Symmetric parts are unchanged when reflected, rotated, or scaled.
  • Tessellation is a 2-dimensional pattern made from plane figures that fit together to fill the plane, leaving no spaces.
  • Triangle is a two dimensional closed figure with three sides.
    • Perpendicular bisectors can be made by joining the vertices and folding between them.
    • Midpoint can be found by folding all three perpendicular bisectors and finding their union, where they cross.
  • Two-dimensional geometric figures include: circle, square, triangle, rectangle, polygon, ...
  • Volume is the amount of space an object occupies.


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