1. •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
2. 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!
3. Triangle
Area = ½b×h
b = base
h = vertical height
Square
Area = a2
a = length of side
Rectangle
Area = b×h
b = breadth
h = height
Parallelogram
Area = b×h
b = breadth
h = height
Trapezoid (US)
Trapezium (UK)
Area = ½(a+b)h
h = vertical height
Circle
Area = πr2
Circumference=2πr
r = radius
Ellipse
Area = πab
Sector
Area = ½r2
θ
r = radius
θ = angle in radians
Area of Plane Shapes
4. Pythagoras' Theorem
Years 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!
Definition
The 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
5. 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.
6. 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.
7. Prisms
Pyramids
Polyhedrons
A polyhedron is a solid made of flat surfaces.
Each surface is a polygon.
Platonic Solids
8. 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!
9. 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.
10. 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.
11. 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.
12. 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.
13. Non-Polyhedron
Some solids have curved surfaces, or a mix of curved
and flat surfaces (so they aren't Polyhedra).
Sphere CylinderCone
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