gec-math

• Basic Geometric Shapes

  • Point
  • Line
  • Segment
  • Ray
• Two Dimensional Shapes


  • Triangles
  • Quadrilaterals
  • Circles
• Triangles


  Three-sided polygons with various types: equilateral, isosceles, and scalene
• Quadrilaterals


  Four sided polygons including squares, rectangles, parallelograms, and trapezoids
• Circles

  Perfectly round shapes with a fixed radius
• The sum of the angles in a triangle is always 180 degrees
• ∠𝐴 + ∠𝐵 + ∠𝐶 = 180
• Pythagorean Theorem


  For a right triangle, the sum of the squares of the two sides is equal to the square of the longest side the hypotenuse
• Quadrilaterals


  • Square
  • Rectangle
  • Parallelogram
  • Trapezoid
• Square


  All sides are equal, and all angles are right angles
• Rectangle


  Opposite sides are equal, and all angles are right angles
• Parallelogram


  Opposite sides are equal, and opposite angles are equal
• Trapezoid

  Has one pair of parallel sides
• Parts of a Circle


  • Radius
  • Diameter
  • Circumference
• Three-Dimensional Shapes

  • Rectangular Prism
  • Cylinder
  • Sphere
  • Cone
• Rectangular Prism


  A three-dimensional shape with six rectangular faces
• Cylinder


  A shape with two circular bases and a curved surface
• Sphere


  A perfectly round three-dimensional shape with all points equidistant from the center
• Cone


  A three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex
• Formulas for Volume of 3D Shapes

  • Rectangular Prism: V = l×w×h
  • Cylinder: V = πr^2h
  • Sphere: V = 4/3 πr^3
  • Cone: V = 1/3 πr^2h
• Formulas for Surface Area of 3D Shapes


  • Rectangular Prism: SA = 2lw + 2lh + 2wh
  • Cylinder: SA = 2πr^2 + 2πrh
  • Sphere: 4πr^2
  • Cone: SA = πr^2 + πrl
• Geometric Transformation


  Operations that change the position, size, or orientation of shapes while preserving their basic properties
• Pre-image


  Figure before the transformation
• Image


  Figure after the transformation
• Classifications of Transformation

  • Rigid - preserves the size and shape
  • Non-rigid - preserves shape but not size
• Types of Transformations

  • Translation
  • Reflection
  • Rotation
  • Dilation
• Translation


  A rigid transformation in which a shape is moved vertically, horizontally, or both
• Reflection


  A rigid transformation in which a shape is mirrored across a line called the line of reflection
• Rotation


  A rigid transformation in which a shape is turned a certain number of degrees around a given point
• Dilation


  A rigid transformation in which a shape made bigger or smaller by a given factor called the scale factor
• Symmetry


  Means that one shape becomes exactly like another when you move it in some way: turn, flip, or slide
• Reflection Symmetry


  Is formed when a figure is divided by a line so that the part on one side of that line is the mirror image of the part of the figure on the other side
• Rotational Symmetry


  The figure remains unchanged when rotated about their center by certain angle
• Patterns

  • Rosette Pattern
  • Frieze Pattern
  • Wallpaper Patterns (Tessellations)
• Rosette Pattern


  Describes the symmetries of a figure rotating by 360 degrees about its center
• Types of Rosette Patterns

  • Dihedral Symmetry
  • Cyclic Symmetry
• Dihedral Symmetry


  Rotation symmetry around a center point with mirror lines through the center point
• Cyclic Symmetry


  Rotation symmetry only around a center point
• Types of Frieze Patterns

  • Hop
  • Step
  • Sidle
  • Spinning Hop
  • Spinning Sidle
  • Jump
  • Spinning jump
• Hop


  Translation only