Question

for how many correspondence between the vertices of two equilateral triangles are similar

Answer 1

Triangles are plane figures determined by three non-collinear points called "vertices." They are made up of the segments, called sides, which join them. Although the sides are segments rather than rays, each pair of them makes up one of the triangle's angles.

Triangles may be classified by the size of their angles or by the lengths of their sides. Triangles whose angles are all less than right angles are called "acute." Those with one right angle are "right" triangles. Those with one angle larger than a right angle are "obtuse." (In a right triangle the side opposite the right angle is called the "hy potenuse" and the other two sides "legs.") Triangles with no equal sides are "scalene" triangles. Those with two equal sides are "isosceles." Those with three equal sides are "equilateral." There is no direct connection between the size of the angles of a triangle and the lengths of its sides. The longest side, however, will be opposite the largest angle; and the shortest side, opposite the smallest angle. Equal sides will be opposite equal angles.

In comparing triangles it is useful to set up a correspondence between them and to name corresponding vertices in the same order. If CXY and PST are two such triangles, then angles C and P co