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Writting in Geometry
Writting in Geometry
In a triangle there are vertex, sides and interior angles.
We use capital letters for vertexes (A, B, C,...), short letters for sides (a, b, c,...) and greec letters for angles. It's usual to have a vertex name and its oposite side with the same letter. We use the clockwise direction in order to name the vertex.
Similar shapes
Similar shapes
Two geometrical objects are similar when one is the result of enlarging or shrinking the other, corresponding angles are equal and the length of corresponding segments are in the same ratio.
We call homologous side or angle, to this side or angle that is equivalent to an other one in an other shape. For example, the text "arrigorriga" in the first image is homologous to the text "arrigorriaga" in the second one.
If two shapes are identical, even if they are turned or translated, we say that thy are congruents.
In the pictures we can see the logo of our high school two times bigger one to the other. For example, the smile of the bulb is twice smaller in the first image than in the second one.
Maps and Scales
Maps and Scales
Maps are representations of an area. There is a scale, the ratio between the real objet and the map, and then we can know the real distance between two points.
For example, in the picture we can see that in the first map 1cm equals to 160 km and in the second map, for instance, 1cm equals to 13 km.
Thales's Theorem
Thales's Theorem
If we have three parallel straight lines, a, b and c, and they cut other two ones, r and r’, then they produce proportional segments :
There are three rules to see if a triangle is similiar to an other one. For this purpose we will use S for sides and A for angles, so that we can rememember properly the ideas.
1st similarity rule: SSS
1st similarity rule: SSS
2nd similarity rule: AAA
2nd similarity rule: AAA
3rd similarity rule: SAS
3rd similarity rule: SAS
Pithagoras' Theorem
Pithagoras' Theorem
In a right angled triangle: the area of an square drawn of the hypotenuse is equal to the sum of the areas drawn in a squares of the other two sides (called catetus).
a2+b2=c2
a2+b2=c2
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