Question

Помогите плиз. 1.В четырехугольнике ABCD диагональ AC разбивает его на два равных треугольника BAC и DAC.Известно что угол BAC равен 30 градусов а угол BCA 40 градусов. Определите углы параллелограмма 2.Из вершины тупого угла ромба равного 120 градусов проведена высота которая отсекает от стороны отрезок в 2см.докажите что высота является биссекстрисой угла образованного диагональю и стороной ромба.Пожалуйста помощь нужна! :(

Answer 1

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Answer 2

Question 1:

In quadrilateral ABCD, diagonal AC divides it into two equal triangles BAC and DAC. It is known that angle BAC is 30 degrees and angle BCA is 40 degrees. Determine the angles of the parallelogram.

To solve this problem, we can use the fact that opposite angles in a parallelogram are equal. Since AC divides the quadrilateral into two equal triangles, we can conclude that angle CAD is also 30 degrees (since triangle DAC is isosceles). Similarly, angle CDA is 40 degrees (since triangle BAC is isosceles).

Therefore, the angles of the parallelogram are as follows: - Angle BAC = 30 degrees - Angle BCA = 40 degrees - Angle CAD = 30 degrees - Angle CDA = 40 degrees

Note: The sum of the angles in a quadrilateral is always 360 degrees.

Question 2:

From the vertex of an obtuse angle of a rhombus, which is equal to 120 degrees, a height is drawn that cuts off a segment of 2 cm from the side. Prove that the height is the bisector of the angle formed by the diagonal and the side of the rhombus.

To prove that the height is the bisector of the angle formed by the diagonal and the side of the rhombus, we need to show that it divides the angle into two equal parts.

Let's consider the given information: - The angle of the rhombus is 120 degrees. - The height cuts off a segment of 2 cm from the side.

To prove that the height is the bisector of the angle, we can use the properties of a rhombus. In a rhombus, the diagonals are perpendicular bisectors of each other. This means that the height, which is perpendicular to the side, will also be perpendicular to the diagonal.

Since the height is perpendicular to the diagonal, it forms a right angle with the diagonal. Therefore, the angle formed by the diagonal and the side of the rhombus is divided into two equal parts by the height, making it the bisector of the angle.