Square and Circle and their Properties — Geometric Stuff

When we study the shapes, we often mention “geometric properties” — do not be scared by the words “properties”, its just some sure-things about a shape, like “circle is round”.

This is a fairly simple graph about the shapes.As shown, ABDE is the square; CSquareCircCirc - 1 is its centre, and the circle centred at C passes through all the four corners: points A, B, D and E.


Here are a number of properties about the square, and its circum-circle: (the circle passing through every corner of the square)

1) The four sides of a square are congruent (equal in length).

2) Each of the interior angle (at the corner) of the square is a right angle, thus these interior angles are congruent.

3) Each square has a centre, which is the intersection point of the two diagonals.

4) The two medians (traversal of the opposite sides) intersect at the centre.

5) The two diagonals of a square bisects each other.

6) Each diagonal divides the square into two regions with equal area, and the two diagonals divide the square into four equal-area regions.

7) Each square is inscribed into a circle, with the centre of circle to be located at centre of the square.

8) For any square, when rotating by 90 degrees, new square will be coincident (overlapping exactly) to the old square. This is true when rotating by any multiples of 90 degrees (since we can apply rotation again and again).


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