2D Shapes Properties and Classification

2D Shapes

Properties and Classification

• Types of 2D shapes:
  • Polygon: a closed shape with 3 or more sides (e.g., triangle, quadrilateral, pentagon)
  • Circle: a continuous curved shape
  • Curve: a continuous curved shape that is not a circle
• Properties:
  • Number of sides
  • Number of angles
  • Type of angles (acute, obtuse, right, straight)
  • Symmetry (line, rotational, or none)

2D Shape Types

• Triangle:
  • 3 sides
  • 3 angles
  • Can be classified as:
    • Equilateral (equal sides)
    • Isosceles (two equal sides)
    • Scalene (no equal sides)
• Quadrilateral:
  • 4 sides
  • 4 angles
  • Can be classified as:
    • Rectangle (all angles are right angles)
    • Square (all sides are equal and all angles are right angles)
    • Rhombus (all sides are equal, but not all angles are right angles)
    • Trapezoid (two pairs of opposite sides are not equal)
• Other 2D Shapes:
  • Pentagon (5 sides)
  • Hexagon (6 sides)
  • Octagon (8 sides)

3D Shapes

Properties and Classification

• Types of 3D shapes:
  • Polyhedra: a closed shape with flat faces and straight edges (e.g., cube, pyramid, prism)
  • Curved shapes: a continuous curved shape (e.g., sphere, cylinder, cone)
• Properties:
  • Number of faces
  • Number of edges
  • Number of vertices
  • Type of faces (triangular, quadrilateral, polygonal)

3D Shape Types

• Polyhedra:
  • Cube:
    • 6 square faces
    • 12 edges
    • 8 vertices
  • Pyramid:
    • 1 base (polygon) and multiple triangular faces
    • 1 apex (vertex)
  • Prism:
    • 2 identical polygon bases
    • Rectangular faces connecting the bases
• Curved 3D Shapes:
  • Sphere:
    • Continuous curved surface
    • All points on the surface are equidistant from the center
  • Cylinder:
    • Two parallel and circular bases
    • Curved lateral surface
  • Cone:
    • Circular base
    • Continuous curved lateral surface
    • Apex (vertex)

2D Shapes

Properties and Classification

• A 2D shape is classified as a polygon if it has 3 or more sides.
• A circle is a continuous curved shape, while a curve is a continuous curved shape that is not a circle.
• Properties of 2D shapes include:
  • Number of sides
  • Number of angles
  • Type of angles (acute, obtuse, right, straight)
  • Symmetry (line, rotational, or none)

2D Shape Types

Triangles

• A triangle has 3 sides and 3 angles.
• Triangles can be classified as:
  • Equilateral (equal sides)
  • Isosceles (two equal sides)
  • Scalene (no equal sides)

Quadrilaterals

• A quadrilateral has 4 sides and 4 angles.
• Quadrilaterals can be classified as:
  • Rectangle (all angles are right angles)
  • Square (all sides are equal and all angles are right angles)
  • Rhombus (all sides are equal, but not all angles are right angles)
  • Trapezoid (two pairs of opposite sides are not equal)

Other 2D Shapes

• A pentagon has 5 sides.
• A hexagon has 6 sides.
• An octagon has 8 sides.

3D Shapes

Properties and Classification

• A 3D shape is classified as a polyhedra if it has flat faces and straight edges.
• A 3D shape is classified as a curved shape if it has a continuous curved surface.
• Properties of 3D shapes include:
  • Number of faces
  • Number of edges
  • Number of vertices
  • Type of faces (triangular, quadrilateral, polygonal)

3D Shape Types

Polyhedra

Cube

• A cube has 6 square faces.
• A cube has 12 edges.
• A cube has 8 vertices.

Pyramid

• A pyramid has 1 base (polygon) and multiple triangular faces.
• A pyramid has 1 apex (vertex).

Prism

• A prism has 2 identical polygon bases.
• A prism has rectangular faces connecting the bases.

Curved 3D Shapes

Sphere

• A sphere has a continuous curved surface.
• All points on the surface of a sphere are equidistant from the center.

Cylinder

• A cylinder has two parallel and circular bases.
• A cylinder has a curved lateral surface.

Cone

• A cone has a circular base.
• A cone has a continuous curved lateral surface.
• A cone has an apex (vertex).

2D Shapes

• 2D shapes have 2 dimensions and at least 3 sides.
• Examples of 2D shapes include triangles, quadrilaterals, polygons, and circles.
• Key features of 2D shapes include:
  • Vertices (corner points)
  • Edges (line segments between vertices)
  • Angles (formed by two adjacent edges)
  • Perimeter (distance around the shape)

Types of 2D Shapes

• Regular 2D shapes have equal sides and angles, such as equilateral triangles, squares, and circles.
• Irregular 2D shapes have unequal sides and angles, such as scalene triangles, rectangles, and trapezoids.

3D Shapes

• 3D shapes have 3 dimensions and at least 4 faces.
• Examples of 3D shapes include tetrahedrons, cubes, rectangular prisms, and spheres.
• Key features of 3D shapes include:
  • Vertices (corner points)
  • Edges (line segments between vertices)
  • Faces (flat surfaces bounded by edges)
  • Volume (amount of space inside the shape)

Types of 3D Shapes

• Polyhedra are 3D shapes with polygon faces, such as tetrahedrons, cubes, and rectangular prisms.
• Non-polyhedra are 3D shapes with curved faces, such as spheres, cylinders, and cones.

Relationships Between 2D and 3D Shapes

• A 2D shape can be a face of a 3D shape.
• A 3D shape can be projected onto a 2D shape, creating a shadow or silhouette.
• 2D shapes can be used to construct 3D shapes, such as building a pyramid from a square base.