•Definition of Geometry. Introduction.•Area of plane shapes. Activities.•Pythagoras’ s Theorem.•Solid Geometry.•Faces, Vertices and Edges. Using of Solids.

Carmen María Aparicio Olea

Geometry

Geometry is all about shapes and their properties. The two most common subjects are: Plane Geometry (is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper)    

Solid Geometry (is about three dimensional objects like cubes and pyramids). If you like playing with objects, or like drawing, geometry is for you!

TriangleArea = ½b×h

b = baseh = vertical height

 Square

Area = a2

a = length of side

RectangleArea = b×hb = breadthh = height

 

ParallelogramArea = b×hb = breadthh = height

Trapezoid (US)Trapezium (UK)Area = ½(a+b)h

h = vertical height

 

CircleArea = πr2

Circumference=2πrr = radius

EllipseArea = πab

 

SectorArea = ½r2θ

r = radiusθ = angle in radians 

Area of Plane Shapes

Pythagoras' TheoremYears ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) ...... and you made a square on each of the three sides, then ...... the biggest square had the exact same area as the other two squares put together!

DefinitionThe longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²): a2 + b2 = c2

Example

Solid Geometry

A face is any of the individual surfaces of a solid object.

An edge is the line where two surfaces meet.

A vertex is the point where edges are crossing.

Solid Geometry

Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...

Three Dimensions It is called three-dimensional, or 3D because there are three dimensions: width, depth and height.  

Prisms

Pyramids

PolyhedronsA polyhedron is a solid made of flat surfaces. Each surface is a polygon.

Platonic Solids

Tetrahedron 4 Faces 4 Vertices 6 Edges

The tetrahedron also has a beautiful and unique property ... all the four vertices are the same distance from each other!

Cube 6 Faces 8 Vertices 12 Edges

A cube is called a hexahedron because it is a polyhedron that has 6 (hexa- means 6) faces.Cubes make nice 6-sided dice, because they are regular in shape, and each face is the same size.

Octahedron 8 Faces 6 Vertices 12 Edges

It is called an octahedron because it is a polyhedron that has 8 (octa-) faces, (like an octopus has 8 tentacles)

If you have more than one octahedron they are called octahedra.

Dodecahedron 12 Faces 20 Vertices 30 Edges

It is called a dodecahedron because it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12).

If you have more than one dodecahedron they are called dodecahedra.

Icosahedron 20 Faces 12 Vertices 30 Edges

It is called an icosahedron because it is a polyhedron that has 20 faces (from Greek icosa- meaning 20).If you have more than one icosahedron they are called icosahedra.

Non-Polyhedron

Some solids have curved surfaces, or a mix of curved and flat surfaces (so they aren't Polyhedra).

Sphere CylinderCone