Are triangles ABC and A1B1C1 similar if AB = 1m, AC = 1.5m, BC = 2m, A1B1 = 10 cm, A1C1 = 15 cm, B1C1 = 20cm?

Similar triangles are triangles in which the angles are respectively equal, and the sides of one are respectively proportional to the sides of the other triangle.

In order to determine whether these triangles are similar, you need to calculate the coefficient of similarity of their sides.

The similarity coefficient is the number k equal to the ratio of the similar sides of similar triangles.

k1 = A1B1 / AB;

k1 = 10/1 = 10;

k2 = В1С1 / ВС;

k2 = 15 / 1.5 = 10;

k3 = A1C1 / AC;

k3 = 20/2 = 10;

k1 = k2 = k3.

Answer: these triangles are similar, since their sides are correspondingly proportional, and the coefficient of their similarity is 10.