Читать книгу Geometry for Students and Parents - Sergey D Skudaev - Страница 13

If all three sides of a triangle are equal, such a triangle is called an equilateral triangle.

What is true for an isosceles triangle is true for an equilateral triangle as well.

Additionally, all three angles of an equilateral triangle are an equal 60 degrees. See figure 24.

Figure 24. An equilateral triangle. Angles A, B and C = 60 degrees.

AB = BC=AC

Bisectors drawn from each angle of an equilateral triangle are altitudes and medians at the same time. A median, an altitude or an angle bisector divides an equilateral triangle into two equal triangles with the angles 30, 60 and 90 degrees. See figure 25.

Figure 25. An equilateral triangle ABC.

BD is a bisector, altitude and median. Triangles ABD and BDC are equal.