How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts? Class 6

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts? Class 6

Question 1.

How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts? Class 6

Solution:

The rectangle should be constructed in such a way that all its sides are equal. In other words, this rectangle must be a square.

Question 2.

What general laws did you observe with respect to the angles and sides? Try to frame and discuss them with your classmates.

How can one be sure if the laws that you have observed will always be true? Class 6

Solution:

On exploration, it is observed that “If all sides of rectangle are equal, then all the eight small angles (that is angles formed by each diagonal with the side of the rectangle) are equal to 45°.” Further, the angle between the two diagonals is a right angle and this rectangle is a square. At this stage, one can only be sure about the laws by verification with the help of measurement. In the later stage (classes), these laws can be logically proved.