CREATING WITH TRIANGLES

This will be the first CREATIVE work you do with Geometry this year:

How can you express yourself when drawing triangles?

You now know the difference between ABSTRACT and FIGURATIVE.
You also know the difference between MEANING and SENSATION.

So, get ready to express yourself with a drawing with triangles.


There are many ideas you can choose:

-A landscape (FIGURATIVE):

 

-A sensation (ABSTRACT)

-A pattern (used to cover surfaces: it is usually abstract, but can also be figurative)

-A word (you will have to transform shapes into triangles)



You can do this work in several ways: painting with colours, or just pencil.
Col-lage is also a thecnic you may use.
Crayons, markers,,,every materials for colouring are welcome.


FEEL FREE to do whatever you want...USING TRIANGLES.

TRIANGLE CONSTRUCTION



http://www.mathopenref.com/consttrianglesss.html

1)Draw all sides (or angles) with your ruler.
2)Start with one side, it doen´t matter which: draw the first side.
3)Take the second side with your compass (no matter which) and draw an arc from the end of the first side.
4)Take the third side with your compass and draw, from the another end of the first side.
5)Close the triangle: join the third point (given by both arcs). Draw the other two sides.

6)REMEMBER that there can be more than one solution for each exercise!


EXERCISES:

1)a=3cm, b=3cm, c=3cm.

2)a=4cm, b=5cm, c=6cm.

3)a=2.5cm, b=c=5cm.

4)a=5cm, b=4.5cm, c=4cm.

Creative triangles: some examples.

Take a look at the next images, that show creations based on triangles:

Here triangles have been organised in a GRID, to construct geometrical shapes:

This is a painting about triangles.

Is it figurative or abstract?

Can you feel its meaning?

This is another (different) painting.

Is it abstract or figurative?

What is it talking about?

Do you feel any sensation when you watch it?

Also triangles can be used to construct new shapes...

this portrait is done with small triangles.

Another expressive painting with triangles.

What sensation do you get?

And the last one:

Does this have a meaning?

Can you find parallel lines?

How many color tones do you see?

What sensation do you get?

TRIANGLE TYPES

According to their angles and sides, triangles can be classified as:

With this theory will be enough. Do you find it interesting? 

Check this shape and count HOW MANY TRIANGLES are therein?

???????????????????????????????

TRIANGLES-Definition

A triangle, as you might know, is a geometrical shape (polygon) with three sides. 

Every triangle has three SIDES and three ANGLES.

Those three angles ALWAYS ADD to 180º : (α + β + γ = 180º)

What´s the name of the three sides of this triangle?

___   ___   ___

AB, BC, CA

All sides are segments, but are also called after one small letter,

which is the same than the opposite vertex.

We use then : 

                    ____

c instead of AB,

                     ____

a instead of BC

                ____

and b instead CA .

You have to know also that ANGLES are named after greek letters:

A=α  Β=β  C=γ     (α + β + γ = 180º)

You must know them. That way names and formulas become easier for you, dear students.

Now, some questions for you to discover:

DO YOU KNOW how many triangles do exist?

CAN YOU find examples for triangles IN NATURE? 

...and in HUMAN WORLD? 

IS THERE any triangle with more/less than 180º angles?