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# Content

```Geometric Shapes Types of Geometric Shapes 2D Geometric Shapes  Triangle Geometric Shapes   Equilateral Triangle   Isoscles Triangle   Scalene Triangle   Right Triangle   Obtuse Triangle   Acute Triangle  Quadrilateral Geometric Shapes   Square   Rectangle   Rhombus   Parallelogram   Trapezoid US/(Trapezium UK)   Kite   Trapezium US (Trapezoid UK)   Polygon   Convex and Concave Polygons   Regular and Irregular Polygons   Types of Polygons  Curved Geometric Shapes   Circle     Semi-Circle Quarter-Circle Circular Sector Circular Segment    Ellipse   Crescent 3D Geometric Shapes  Cube  Cuboid  Box  Sphere  Ellipsoid  Cylinder  Cone  Triangular Prism  Hexagonal Prism  Triangular-based Pyramid  Square-based Pyramid  Hexagonal Pyramid  The 5 Platonic Solids   Tetrahedron   Cube (regular hexahedron)   Octahedron   Dodecahedron   Icosahedron```

# Geometric Shapes

Geometric Shapes is figure or area enclosed by a boundary. A boundary is created by jointing geometric elements, e.g. curves, points, lines, and surfaces together.

## 2D Geometric Shapes

### Triangle Geometric Shapes

#### Equilateral Triangle

Equilateral triangles have all angles equal to 60° and all sides equal length. All equilateral triangles have 3 lines of symmetry.

#### Isoscles Triangle

Isosceles triangles have 2 angles equal and 2 sides of equal length. All isosceles triangles have a line of symmetry.

#### Scalene Triangle

Scalene triangles have no angles equal, and no sides of equal length.

#### Right Triangle

Right triangles (or right angled triangles) have one right angle (equal to 90° ).

#### Obtuse Triangle

Obtuse triangles have one obtuse angle (an angle greater than 90° ). The other two angles are acute (less than 90° ). Oblique - One angle greater than 90°

#### Acute Triangle

Acute triangles have all angles acute.

#### Square

Squares have 4 equal sides and 4 right angles. They have 4 lines of symmetry. All squares belong to the rectangle family. All squares belong to the rhombus family. All squares are also parallelograms.

#### Rectangle

Rectangles have 4 sides and 4 right angles. They all have 2 lines of symmetry (4 lines if they are also a square!) All rectangles belong to the parallelogram family.

#### Rhombus

Rhombuses (rhombii) have 4 equal sides. Both pairs of opposite sides are parallel. They all have 2 lines of symmetry (4 lines if they are a square!) All rhombuses belong to the parallelogram family.

#### Parallelogram

Parallelograms have 2 pairs of parallel sides. Some parallelograms have lines of symmetry (depending on whether they are also squares, rectangles or rhombuses), but most do not.

#### Trapezoid US/(Trapezium UK)

Trapezoids US (Trapeziums UK) have one pair of parallel sides. Some trapezoids have a line of symmetry. Please note the differences between the definitions for US and UK.

#### Kite

Kites have 2 pairs of equal sides which are adjacent to each other.

#### Trapezium US (Trapezoid UK)

Trapeziums US (Trapezoids UK) are quadrilaterals with no parallel sides. Please note the differences between the definitions for US and UK.

### Polygon

#### Convex and Concave Polygons

Polygons can be concave or convex in their shape. Convex shapes have all angles less than 180° Concave shapes have at least one reflex angle greater than 180° Triangles are always convex.

#### Regular and Irregular Polygons

Here is a list of regular polygons from 3 to 10 sides. For each polygon, a regular and an irregular example have been shown. Any regular shape will be mathematically similar to the example shown (having the same angles). Regular shapes are always convex. Irregular shapes can be concave or convex.

#### Types of Polygons

Pentagon Hexagon Heptagon Octagon Decagon N-gon

### Curved Geometric Shapes

#### Circle

Circles have a point in the centre from which each point on the diameter is equidistant. They have infinite lines of symmetry. How many sides does a circle have? This is an interesting question - the answer could be 0 (no straight sides), 1 curved side, or an infinite number of sides are all possible answers.

#### Ellipse

Ellipses are like circles which have been squashed or stretched. They have 2 lines of symmetry. They are also a special type of oval. The longest and shortest diameters of the ellipse are called the major and minor axes. These axes are also the lines of symmetry.

#### Crescent

Crescent shapes are made when two circles overlap, or when one circle is removed from another circle . The perimeter of crescents are made from two circular arcs. They have 1 line of symmetry. Our moon forms crescent shapes during its phases. Some countries such as Turkey or Algeria have crescent shapes on their flags.

## 3D Geometric Shapes

### Cube

Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid.

### Cuboid

Cuboids have 6 faces, 12 edges and 8 vertices. All the faces on a cuboid are rectangular.

### Sphere

Spheres have either 0 or 1 faces, 0 edges and 0 vertices.

### Ellipsoid

Ellipsoids have either 0 or 1 faces, 0 edges and 0 vertices.

### Cylinder

Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices.

### Cone

Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex (which is described by some mathematicians as a vertex).

### Triangular Prism

Triangular Prisms have 5 faces, 9 edges, and 6 vertices. The two faces at either end are triangles, and the rest of the faces are rectangular.

### Hexagonal Prism

Hexagonal Prisms have 8 faces, 18 edges, and 12 vertices. The two faces at either end are hexagons, and the rest of the faces are rectangular.

### Triangular-based Pyramid

Triangular-based pyramids have 4 faces, 6 edges and 4 vertices. The base is a triangle. All of the faces are triangular. If the triangular faces making up the prism are all equilateral, then the shape is also called a Tetrahedron.

### Square-based Pyramid

Square based pyramids have 5 faces, 8 edges and 5 vertices The base is a square. All the other faces are triangular.

### Hexagonal Pyramid

Hexagonal pyramids have 7 faces, 12 edges, and 7 vertices. The base is a hexagon. All of the other faces are triangular.

### The 5 Platonic Solids

The platonic solids form a set of 5 polyhedra with the following special properties: the faces of the platonic solids have to be regular and congruent. the same number of faces meet at each vertex. They are named after the Greek philosopher Plato who wrote about them in his philosophical discussions. There are only 5 platonic solids: Regular tetrahedron Cube or regular hexahedron Regular octahedron Regular dodecahedron Regular icosahedron

#### Tetrahedron

A Tetrahedrons is the same as a triangular pyramid. They have 4 triangular faces, 6 edges and 4 vertices. A regular tetrahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.

#### Cube (regular hexahedron)

Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid and is one of the 5 platonic solids.

#### Octahedron

Octahedrons are a shape with 8 faces, 12 edges and 6 vertices. A regular octahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.

#### Dodecahedron

Dodecahedrons are a shape with 12 faces, 30 edges and 20 vertices. A regular dodecahedron has regular pentagons for its faces, and is one of the 5 platonic solids.

#### Icosahedron

Icosahedron are a shape with 20 faces, 30 edges and 12 vertices. All the faces are triangles. A regular icosahedron is one of the 5 platonic solids with all faces being equilateral triangles.

ID: 210300010 Last Updated: 3/10/2021 Revision: 0 Ref: References

1. Hilbert, D. (translated by Townsend E.J.), 1902, The Foundations of Geometry
2. Moore, E.H., 1902, On the projective axioms of geometry
3. Fitzpatrick R. (translated), Heiberg J.L. (Greek Text), Euclid (Author), 2008, Euclid's Elements of Geometry  Home 5

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