Properties of 2D Shapes

2D Shapes

Properties

• Number of sides (e.g., triangle: 3, quadrilateral: 4, pentagon: 5)
• Number of angles (e.g., triangle: 3, quadrilateral: 4)
• Types of angles: acute, obtuse, right, straight, reflex
• Sum of interior angles:
  • Triangle: 180°
  • Quadrilateral: 360°
  • Pentagon: 540°
  • Hexagon: 720°
• Symmetry: line of symmetry, rotational symmetry

Types of 2D Shapes

• Triangles:
  • Equilateral: all sides equal
  • Isosceles: two sides equal
  • Scalene: all sides unequal
• Quadrilaterals:
  • Rectangle: opposite sides equal, all angles right
  • Square: all sides equal, all angles right
  • Rhombus: all sides equal, opposite angles equal
  • Trapezium: no equal sides, two pairs of opposite angles
• Polygons:
  • Pentagon: five sides
  • Hexagon: six sides
  • Octagon: eight sides
• Circles:
  • Center: fixed point
  • Radius: distance from center to circle
  • Circumference: distance around circle

3D Shapes

Properties

• Number of faces (e.g., cube: 6, sphere: 1)
• Number of edges (e.g., cube: 12, sphere: 0)
• Number of vertices (e.g., cube: 8, sphere: 0)
• Types of angles: dihedral angles (between faces)

Types of 3D Shapes

• Prisms:
  • Rectangular prism: rectangular faces
  • Triangular prism: triangular faces
• Pyramids:
  • Square pyramid: square base
  • Triangular pyramid: triangular base
• Polyhedra:
  • Cube: six square faces
  • Tetrahedron: four triangular faces
  • Octahedron: eight triangular faces
• Spheres:
  • Surface: curved
  • Center: fixed point
  • Radius: distance from center to surface
• Cylinders:
  • Two parallel and circular bases
  • Curved surface connecting bases
  • Height: distance between bases

2D Shapes

Properties

• A shape's number of sides and angles are related to its type
• Angles can be acute, obtuse, right, straight, or reflex
• The sum of interior angles varies by shape:
  • Triangles: 180°
  • Quadrilaterals: 360°
  • Pentagons: 540°
  • Hexagons: 720°
• Symmetry can be line or rotational

Shape Types

• Triangles:
  • Equilateral: all sides equal
  • Isosceles: two sides equal
  • Scalene: all sides unequal
• Quadrilaterals:
  • Rectangle: opposite sides equal, all angles right
  • Square: all sides equal, all angles right
  • Rhombus: all sides equal, opposite angles equal
  • Trapezium: no equal sides, two pairs of opposite angles
• Polygons:
  • Pentagon: five sides
  • Hexagon: six sides
  • Octagon: eight sides
• Circles:
  • Center: fixed point
  • Radius: distance from center to circle
  • Circumference: distance around circle

3D Shapes

Properties

• Shapes have varying numbers of faces, edges, and vertices
• Dihedral angles exist between faces
• Edges connect vertices

Shape Types

• Prisms:
  • Rectangular prism: rectangular faces
  • Triangular prism: triangular faces
• Pyramids:
  • Square pyramid: square base
  • Triangular pyramid: triangular base
• Polyhedra:
  • Cube: six square faces
  • Tetrahedron: four triangular faces
  • Octahedron: eight triangular faces
• Spheres:
  • Surface: curved
  • Center: fixed point
  • Radius: distance from center to surface
• Cylinders:
  • Two parallel and circular bases
  • Curved surface connecting bases
  • Height: distance between bases

2D Shapes

Properties

• A 2D shape has a fixed number of sides, angles, and types of angles.
• Types of angles include acute, obtuse, right, straight, and reflex.
• The sum of interior angles in a 2D shape depends on the number of sides:
  • Triangle: 3 sides, 3 angles, 180°
  • Quadrilateral: 4 sides, 4 angles, 360°
  • Pentagon: 5 sides, 5 angles, 540°
  • Hexagon: 6 sides, 6 angles, 720°
• A 2D shape can have line symmetry or rotational symmetry.

Types of 2D Shapes

Triangles

• Equilateral triangle: all sides are equal.
• Isosceles triangle: two sides are equal.
• Scalene triangle: all sides are unequal.

Quadrilaterals

• Rectangle: opposite sides are equal, all angles are right.
• Square: all sides are equal, all angles are right.
• Rhombus: all sides are equal, opposite angles are equal.
• Trapezium: no equal sides, two pairs of opposite angles.

Polygons

• Pentagon: a 5-sided polygon.
• Hexagon: a 6-sided polygon.
• Octagon: an 8-sided polygon.

Circles

• A circle has a fixed center point.
• The radius is the distance from the center to the circle.
• The circumference is the distance around the circle.

3D Shapes

Properties

• A 3D shape has a fixed number of faces, edges, and vertices.
• Faces can be rectangular, triangular, or other shapes.
• Edges can be long or short, depending on the shape.
• Vertices can be sharp or blunt, depending on the shape.
• Dihedral angles are the angles between faces.

Types of 3D Shapes

Prisms

• Rectangular prism: a 3D shape with rectangular faces.
• Triangular prism: a 3D shape with triangular faces.

Pyramids

• Square pyramid: a 3D shape with a square base.
• Triangular pyramid: a 3D shape with a triangular base.

Polyhedra

• Cube: a 3D shape with six square faces.
• Tetrahedron: a 3D shape with four triangular faces.
• Octahedron: a 3D shape with eight triangular faces.

Spheres

• A sphere has a curved surface.
• The center is a fixed point.
• The radius is the distance from the center to the surface.

Cylinders

• A cylinder has two parallel and circular bases.
• The curved surface connects the bases.
• The height is the distance between the bases.