Question

Диагонали ромба равны 6 и 10.Найдите стороны и углы четырех угольника с вершинами в серединах сторон того ромбаС обьяснениями пожалуйста!

Answer 1

Стороны четырёхугольника равны: 6/2 = 3 и 10/2 = 5

Answer 2

Finding the Sides and Angles of the Quadrilateral

To find the sides and angles of the quadrilateral with vertices at the midpoints of the sides of the given rhombus, we can use the properties of a rhombus and basic geometry principles.

Let's start by labeling the given rhombus and the quadrilateral as follows:

- Rhombus: ABCD, with diagonals AC and BD. - Quadrilateral: EFGH, with vertices at the midpoints of the sides of the rhombus.

Now, let's proceed with the calculations step by step:

Finding the Sides of the Quadrilateral

1. The diagonals of a rhombus bisect each other at right angles. Therefore, the diagonals AC and BD of the rhombus ABCD intersect at a right angle. This means that the quadrilateral EFGH is a rectangle.

2. In a rectangle, opposite sides are congruent. Since the diagonals of the rhombus ABCD bisect each other, the sides of the quadrilateral EFGH are equal to half the lengths of the diagonals of the rhombus.

- Side EF = Side GH = 6/2 = 3 units. - Side FG = Side EH = 10/2 = 5 units.

Finding the Angles of the Quadrilateral

3. In a rectangle, all angles are right angles (90 degrees). Therefore, the angles of the quadrilateral EFGH are all right angles.

- Angle E = Angle F = Angle G = Angle H = 90 degrees.

To summarize, the sides of the quadrilateral EFGH are 3 units and 5 units, and all angles are right angles (90 degrees).

Please let me know if you need any further clarification or assistance!