Question

Укажите номера верных утверждений.    1) Медиана равнобедренного треугольника, проведённая из вершины, противолежащей основанию, перпендикулярна основанию.   2) Диагонали любого прямоугольника делят его на 4 равных треугольника.   3) Для точки, лежащей внутри круга, расстояние до центра круга меньше его радиуса.

Answer 1

I can answer your question in detail. You have to indicate the numbers of the correct statements. Here are the explanations for each statement:

- 1) The median of an isosceles triangle, drawn from the vertex opposite the base, is perpendicular to the base. This statement is true. The median of an isosceles triangle is also the bisector and the height of the triangle, so it divides the base into two equal parts and forms a right angle with it . - 2) The diagonals of any rectangle divide it into four equal triangles. This statement is false. The diagonals of a rectangle are equal and bisect each other, but they do not necessarily divide the rectangle into four equal triangles. The triangles will be equal only if the rectangle is a square, otherwise they will have different areas. - 3) For a point inside a circle, the distance to the center of the circle is less than its radius. This statement is true. The radius of a circle is the longest distance from the center to any point on the circle. Any point inside the circle will have a shorter distance to the center than the radius.

Therefore, the correct answer is 1 and 3. I hope this helps you understand the geometry concepts better.