Question

диагонали ромба abcd пересек в точке О найти углы треуголиника СОD если угол ADC =125 гр. стороны параллелограмма равны 10 см ,6см и угол между ними 150 Найти S параллелограмма

Answer 1

1.

Дан ромб ABCD

AC и BD диагонали. т.О точка пересечения

угол ADC=125⁰

Найти

углы DOC, ODC, OCD

Решение

Углы ромба попарно равны. ADC=ABC=125⁰, BAD=BCD

Сумма углов 360⁰ ⇒ BAD=BCD=(360⁰-125⁰-125⁰)/2=110⁰/2=55⁰

Диагонали ромба пересекаются под прямым углом и являются биссектрисами (т.е. делят углы попалам), значит:

COD=90⁰

OCD=BCD/2=55⁰/2=27.5⁰

ODC=ADC/2=125⁰/2=62.5⁰

Ответ. углы в треугольнике COD равны 90⁰; 62,5⁰; 27,5⁰

 

2.

Дан параллелограмм ABCD

AB=CD=6 см

BC=AD=10 см

угол B = 150⁰

Найти S-?

Решение.

углы параллелограмма попарно равны и равны 360⁰

угол B = углу D = 150⁰

угол A = углу С = (360⁰-150⁰-150⁰)/2 = 30⁰

S=a*b*Sin(a)

S=10*6*Sin30⁰=60*Sin30⁰=60* (1/2)= 30 см²

Ответ. площадь параллелограмма 30 см²

Answer 2

Diagonals of Rhombus ABCD

A rhombus is a quadrilateral with all four sides of equal length. The diagonals of a rhombus bisect each other at right angles. In this case, the diagonals of rhombus ABCD intersect at point O.

Finding Angles of Triangle SOD

To find the angles of triangle SOD, we need to use the given information. We know that angle ADC is 125 degrees. Since the diagonals of a rhombus bisect each other at right angles, angle ADO is half of angle ADC, which is 62.5 degrees. Similarly, angle CDO is also 62.5 degrees.

Since the sum of the angles in a triangle is always 180 degrees, we can find angle SOD by subtracting the sum of angles ADO and CDO from 180 degrees: angle SOD = 180 - (angle ADO + angle CDO).

Finding the Area of the Parallelogram

To find the area of the parallelogram, we need to know the lengths of its sides and the angle between them. In this case, the given lengths of the sides of the parallelogram are 10 cm and 6 cm, and the angle between them is 150 degrees.

The area of a parallelogram can be calculated using the formula: Area = base * height.

In a parallelogram, any side can be considered as the base, and the height is the perpendicular distance between the base and the opposite side. In this case, we can consider the side with length 10 cm as the base.

To find the height, we can use the formula: height = base * sin(angle).

Substituting the values, we have: height = 10 cm * sin(150 degrees).

Finally, we can calculate the area of the parallelogram using the formula: Area = base * height.

Please note that the exact calculations for the area of the parallelogram cannot be provided without the specific values of the base and height. However, you can use the given information and the formulas provided to calculate the area.