Let’s take a look at many of the geometric shapes you will encounter in geometry classes.

We will begin with 2d shapes which have length and width, but no height.

2d shapes include

**polygons**and

**curved shapes**.

3d shapes have height, width, and depth.

These shapes can have straight lines or curves.

Let’s get started by looking at our first type of 2d shapes “polygons”

Polygons are 2-dimensional closed shapes.

Polygons are 2-dimensional closed shapes.

- A closed shape does not have any openings, and all of the lines connect.
- You can’t leave the inside of a closed shape without crossing a line.
- Polygons have straight lines and do not have curves
- A polygon has three parts.
- Straight Lines
- Vertices which are the point at which the lines intercept
- Angles are formed by intercepting lines
- There are several types of polygons
- A regular polygon has equal lines and angles
- An irregular does not have equals lines and angles
- A concave polygon has one angle greater than 180 degrees
- A convex polygon does not have any internal angles greater than 180 degrees
- A simple polygon does not have any lines that cross over.
- A complex polygon has at least one line that crosses over itself

Polygon names

Named after the number of sides and angles

- Triangle 3 sides
- Quadrilateral
- Pentagon 5
- Hexagon 6
- Heptagon 7
- Octagon 8
- Nonagon 9
- Decagon 10
- Hendecagon 11
- Dodecagon 12

After 12 sides it is acceptable to give the number of sides and then gon

For example 14 gon has 14 sides

Curved 2d shapes have curved lines instead of straight lines.

Common examples of curved shapes include a circle,

an ellipse which looks like a circle that has been stretched or squashed

A crescent is also a curved 2d shape

3d shapes are shapes that have height, width, and depth

A sphere and a cone are examples of 3d shapes

Many 3d shapes are considered polyhedrons.

Let’s take a look at the properties of polyhedrons

A polyhedron is a 3D solid figure in which each side is a flat surface composed of polygons.

What is a polyhedron?

- A polyhedron is a 3D solid figure with a flat surface.
- A polyhedron does not have any curved surfaces.
- A polyhedron is derived from poly=many.
- Hedron = Face so it means many faced geometric shape.

Is a Dodecahedron a polyhedron yes

Is a triangle a polyhedron? No It is 2D

Is a sphere a polyhedron? No it has curves

Is a coffee mug a polyhedron? No

Some common examples of a polyhedron are prisms and pyramids

Euler's Polyhedron states that the number of faces + number of vertices = number of edges + 2

A platonic solid is a convex Polyhedron that satisfy these three characteristics

All are regular polygons

All faces are congruent

All corners are congruent. The same number of faces meet at every vertex

3 Platonic solids are made of equilateral triangles

tetrahedron, octahedron, icosahedron

One platonic solid is made of squares.

One platonic solid is made of pentagons.

Tetrahedron

- 3 equilateral triangles at each corner
- 4 triangle faces

Octahedron

- 4 equilateral triangles at each corner
- 8 triangle faces

Icosahedron

- 5 equilateral triangles at each corner
- 20 triangle faces

Dodecahedron

- 3 pentagons at each corner
- 12 pentagon faces

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