"Math Salamanders Free Math Sheets"
Welcome to the Math Salamanders' Geometric Shapes Information Page.
Here you will find a list of different geometric shapes to help you to identify a range of 2d and 3d shapes.
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List of Geometric Shapes
2d Geometric Shapes
Here are our list of 2d geometric shapes, including triangles, quadrilaterals and polygons
List of Geometric Shapes  Triangles
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° ). 
Acute Triangle

Acute triangles have all angles acute. 
Is an Equilateral triangle a special case of an Isosceles triangle?
According to Wikipedia:
" In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. "
Source: https://en.wikipedia.org/wiki/Isosceles_triangle
This means that there is some dispute as to whether an equilateral triangle is a special case of an isosceles triangle or not!
Most modern textbooks include use the 'at least' definition for isosceles triangles.
List of Geometric Shapes  Quadrilaterals
A quadrilateral is a polygon with 4 sides.
Quadrilaterals are also sometimes called quadrangles or tetragons.
There are quite a few members of the quadrilateral family.
There are also some members which are a subset of other members of this family!
See below if this confuses you!
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

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

Trapeziums US (Trapezoids UK) are quadrilaterals with no parallel sides. Please note the differences between the definitions for US and UK. 
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.
Convex hexagon Convex shapes have no reflex angles (angles > 180° ) 
Concave hexagon Concave shapes have at least one reflex angle greater than 180° 
Convex pentagon 
Concave pentagon 
Convex octagon 
Concave octagon 
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.
There are an infinite number of examples of different irregular polygons that could be shown, and only one example is given.
Equilateral Triangle Angle: 60° Interior angles add up to 180° 
Irregular Triangle 
Square Angle: 90° Interior angles add up to 360° 
Irregular Quadrilateral 
Pentagon Angle: 108° Interior angles add up to 540° 
Irregular Pentagon

Hexagon Angle: 120° Interior angles add up to 720° 
Irregular Hexagon 
Heptagon Angle: 128.6° Interior angles add up to 900° 
Irregular Heptagon 
Octagon Angle: 135° Interior angles add up to 1080° 
Irregular Octagon 
Nonagon Angle: 140° Interior angles add up to 1260° 
Irregular Nonagon 
Decagon Angle: 144° Interior angles add up to 1440° 
Irregular Decagon 
Formula for Interior Angles of a Polygon
The formulae for the interior angles of a polygon are as follows:
Total of interior angles = 180 x (number of sides  2)
Interior Angle of a regular polygon = total of interior angles / number of sides
Example
What is the interior angle of a regular pentagon?
Step 1) Total of interior angles is 180 x (number of sides  2)
= 180 x (5  2) = 180 x 3 = 540 °
Step 2) The interior angle = total of interior angles ÷ number of sides = 540 ÷ 5 = 108 °
Answer: 108 °
List of Geometric Shapes  Curved 2d Shapes
Here are some curved 2d shapes which have not yet been included.
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. 
List of Geometrics Shapes  3D Shapes
Here are some common 3D shapes that you should know.
Along with a picture of each shape, the number of faces, edges and vertices are also given.
Common properties of the 3D shapes are also given.
Please note that there is some disagreement over the definitions and properties of 3d shapes.
Some mathematicians allow a face to be curved and some do not.
Some mathematicians allow an edge to be curved and some do not.
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. 
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. 
Triangularbased Pyramid 
Triangularbased 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. 
Squarebased 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:
They are named after the Greek philosopher Plato who wrote about them in his philosophical discussions.
There are only 5 platonic solids:
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. 
Printable List of Geometric Shapes 2D
Here you will some printable 2d shape sheets showing a range of 2d shapes.
You can choose to have the properties of the 2d shapes displayed or not.
The sheets have been split up into US shapes and UK shapes, as there is a difference in the terminology used.
Printable Geometric Shapes 3D
Here you will some printable 3 d shape sheets showing a range of 3d shapes.
You can choose to have the sheet printed in color or black.
More Printable Shape Sheets  2D & 3D Shape Sheets
Here you will find a selection of printable 2d and 3d shape sheets.
Each sheet is available in color or black and white, and labelled or unlabelled.
Using these sheets will help your child to:
Geometry Formula Sheet
Here you will find our support page about different Geometry formulas, including formulas about triangles, circles, quadrilaterals and polygons, as well as 3d shape formulae.
In the Geometry Cheat Sheet section you will find a range of printable geometry sheets with formula and information about angles, 2d and 3d shapes.
Using these sheets will help your child to:
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