How to find the coefficient of similarity of triangles

Similar shapes are shapes that are the same in shape but different in size.Triangles are similar if their angles are equal and sides are proportional to each other. There are also three features to determine the similarity without complying with all conditions. A sign with two similar triangles two angles of the one equal to two angles of the other. The second feature of similarity of triangles two sides of one proportional to two sides of the other, and the angles between these sides have their equal. The third feature of similarity is the proportionality of the three sides of one to three sides of another.

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.