The triangle is the simplest polygon which school students on a geometry course meet. During its study it is possible to push off with the concept "similarity" which defines two figures with equal corners. One of parameters of similar triangles is the similarity coefficient.
Instruction
1. Check whether triangles are similar on the first sign. This sign shows that triangles are similar in case two corners of one polygon are equal to two corners of another. The proof of this rule appears the second theorem of equality of triangles. For definition of it it is necessary to use a protractor. Apply its central part to a corner point so that the lower part was parallel or coincided with one of the parties of a figure. The corner is equal to that value to which the second party points. Thus measure four corners and compare.
2. Calculate a ratio of two parties of one triangle to the relevant parties of another. If values of a proportion were equal and corners between the parties are identical, then triangles are considered as similar. So the second sign of similarity says. For the proof of this rule it is necessary to accept to value which is equal to the relation of the similar parties of a triangle of ABC and A1B1C1.
3. By means of a homothety with any center it is necessary to construct the third triangle of A2B2C2 which two parties will be equal to the parties of the first triangle increased on "to" and a corner between them it will be observed. If A1B1C1 and A2C2B2 are equal on the first sign of equality of triangles, then initial figures are considered as similar.
4. Define a ratio of all parties of one triangle to the relevant parties of another. At the same time there is no need for measurement of corners. If proportions were equal, then triangles are similar on the third sign. This theorem has the similar proof, as the second sign of similarity. At the same time the third figure is under construction on all three parties.
5. Find similarity coefficient for two triangles. It is equal to the relation of the skhodstvenny parties of similar triangles.