You will need

- - handle;
- paper for records.

Instruction

1

*The coefficient*

**of similarity**expresses the proportionality is the ratio of the lengths of the sides of one triangle are congruent to the sides of the other: k = AB/A'b’= BC/B'c’ = AC/A'c’. Congruent sides in the triangles are opposite equal angles.

*The coefficient*

**of similarity**can be found in different ways.

2

For example, a task given to similar triangles and the lengths of their sides. You want to find the ratio

**of similarity**. Since the triangles are similar by condition, find their homologous sides. To do this, write the lengths of the sides of one and the other ascending. Find the ratio of homologous sides, which is the ratio**of similarity**.3

You can calculate coefficient

**of similarity****of triangles**, if you are aware of their area. One of the properties of similar**triangles**States that the ratio of their areas equals the square of the coefficient**of similarity**. Separate the values of the areas of such**triangles,**one for the other and extract the square root of the result.4

The relationship of the perimeters, lengths of the medians of Mediatrix built to congruent sides equal to the ratio

**of similarity**. If you divide the length of the bisectors or altitudes drawn from the same angles, you will also get a coefficient**of similarity**. Use this property to find the coefficient, if the condition of the problem given these values.5

By theorem of sines for any triangle the ratio of sides to sines of opposite angles is equal to the diameter described around the circumference. This implies that in such

**triangles**the ratio of the radii or diameters of the described circle is equal to the ratio**of similarity**. If the task is known, the radii of these circles, or they can figure out areas of circles, find the ratio**of similarity**this way.6

Use the same way to find the coefficient if you have written in similar triangles circles with known radii.