Square
- Author:
- Sarah Keistler
To create a square we first need to construct circle A using the circle tool. Then we will construct the diameter of the circle. To do this I construct a line through point A and B. Then I marked the point of intersection with the circle and the line and labeled it point C. Then I hide line AB and constructed line segment CB. Next I constructed a perpendicular bisector to line CB. This will be a line that divided segment CB into equal halves at a right angle. I labeled the points of intersection with the circle and the perpendicular bisector points D and E. From here we see that we have a 4 sided polygon BDCE. Using the angle measure tool we can see that the interior angles of the polygon are equal. We can also see that the distance of the sides are also equal and therefore the 4 sided polygon is a square. We also know that angle is a right angle from the inscribed angle theorem. The arc that this angle is inscribed in is a semi circle that measures and therefore the inscribed angle measures . This is true of angles . Therefore we have a polygon with four equal right angles. Since the diagonals of the polygon are both radii of the circle they measure equal length. From properties of squares we know that the diagonals of a square are equal. So since this four sided polygon has four right angles and two diagonals of equal length, we can conclude that this is a square.