Question

может ли прямоугольный треугольник быть а)равнобедренным б)равносторонним? обязательно с доказательством,но без теоремы пифагора

Answer 1

прямоугольный треугольник может быть равнобедренным с углами при основании по 45 градусов и вершиной в 90 градусов.

Он не может быть равносторонним, потому, что у равностороннего треугольника все углы равны 60 градусам.

Answer 2

Can a Right-Angled Triangle Be:

a) Isosceles (Equilateral)? b) Equilateral (Equiangular)?

A right-angled triangle can be: a) Isosceles (having two sides of equal length) b) Not Equilateral (having all sides of equal length)

In a right-angled triangle, the sides can be related using the Pythagorean theorem, but I will provide the explanation without using it.

In a right-angled triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called legs. If the two legs of a right-angled triangle are of equal length, then the triangle is an isosceles right-angled triangle. However, the angles of a right-angled triangle are always 30, 60, and 90 degrees, so it cannot be equilateral (having all sides of equal length) unless it is also equiangular (having all angles of equal measure), which is not possible for a right-angled triangle.

The lengths of the sides of a right-angled triangle can be related using various Pythagorean triples, such as 3, 4, 5 and 6, 8, 10. These triples represent the lengths of the sides of right-angled triangles without being equilateral.

Therefore, a right-angled triangle can be isosceles but not equilateral.