Draw a rectangle in which each diagnol=6cm and the acute angle between them is 45
In a rectangle, the two diagonals right-bisect each other.
Since they are equal, and we are told the angle between them is 45°, our rectangle must be a square.
let the side of the square be x
x^2 + x^2 = 6^2
2x^2 = 36
x^2 = 18
x = √18 = 3√2 or appr 4.26 cm
The other way would be to draw 2 lines that are perpendicular. If you have a compass, set the radius at 3 cm and draw a circle. Join the 4 intersection point and you will have your rectangle (square).
The diameter of the circle will be 6 cm, which in turn will be the diagonal of your square.
In a square (or rhombus), the diagonals are perpendicular.
Since your diagonals have a 45° angle between them, the two semi-diagonals form an isosceles triangle with vertex angle 45° and equal sides of length 3.
I expect you can draw that, eh? The length is 5.544 and the width is 2.296
To draw a rectangle where each diagonal measures 6cm and the acute angle between them is 45 degrees, we can follow these steps:
Step 1: Start by drawing a horizontal line segment that will serve as the base of the rectangle. Label its two endpoints as A and B.
Step 2: From point A, draw a perpendicular line segment upward. This will be one side of the rectangle. Label the point where this line intersects the base as C.
Step 3: From point B, draw a line segment parallel to the line segment AC. Extend it until it intersects the perpendicular line. Label this point as D.
Step 4: Now, we need to find the length of the sides of the rectangle. Recall that the length of the diagonals of a rectangle is equal. So, each diagonal will be 6cm.
Step 5: Draw the diagonal line segment AC, which will be 6cm in length. This line will connect points A and C.
Step 6: To find point D, we can use the fact that the acute angle between the diagonals is 45 degrees. Since we have a right triangle ADC with angle C equal to 45 degrees, we can use trigonometry to find the length of AD. Knowing that the adjacent side (AD) is equal to the hypotenuse (6cm) times the cosine of the angle (45 degrees), we can calculate AD.
Step 7: Once we have the length of AD, we can draw a line segment from point D parallel to AC. This line segment will also be equal in length to AD.
Step 8: Connect the remaining points: draw a line segment from D to C. This will be the fourth side of the rectangle.
Step 9: Finally, label the remaining vertices of the rectangle as E (where AD intersects BC) and F (where AC intersects BD).
Following these steps will allow you to draw a rectangle where each diagonal measures 6cm and the acute angle between them is 45 degrees.