Work made by Deva and Lucía (2ºD)

1. proportion
and ratios

2. 1. Similar shapes
Two different figures are similar when they are only different in
size.The corresponding parts are proportional.In other words,
each side of one is obtained by multiplying the same side of the
other by a fixed number called the ratio of similarity
Two shapes are similar if :
● An angle that is measure in the first shape = the same angle
in the second shape
● A proportion in the first shape = the same proportion in the
second shape

3. Worked examples
If we divide any segment of the
second shape by the matching
segment of the first we obtain the
ratio.
The quotient is the ratio of
similarity that change the first
shape into the second shape.
The triangles show the ratio of
similarity as a percentage .

4. 2. Plans,maps and models
● Plans and maps are similar to the reality they represent
.Sizes and distances are important, as well as the
distribution of areas.This is why they have a scale
● The scale is the ratio between each reproduce length
(map,plan or model) and the same length in reality. So, it
is the ratio of similarity between the model and the actual
object.

5. Scale example

6. 2.1 Getting the scale
On the floor plan: 4 cm
In reality: 4 m
So, the scale is 1:100
Now we can measure the
distances on the floor plan
and multiply the results by
100 to get any other real
distance.

7. 3.How to build similar figures.
Projection method
We want to make a figure x times as big. To do this, we take
any point. Draw straight lines that pass through the point.

8. 4.Thales´theorem
If lines A,B and C are parallel and cross two other lines R and
S, then the segments inside are proportional :
AB/BC = A´B´/B´C´

9. Example
AE/EC = BD/DA
8/10 = 5/?
?x8 = 10x5
?X8 = 50
? = 50/8
? = 6,25

10. 5.Applications of similarity of triangles
Calculating the height of a vertical object from its shadow

11. 5.1 Calculate the height of the vertical object without
using its shadow The boy looks to the highest point of the tree
the right angled triangle with sides a,b and c
are similar because they are in Thales
position.
EXAMPLE:
C/D = B/A
To make this problem we need to know c
and b to calculate a.
The height of the tree is equal to c

12. Thanks for your attention