Construction of Square
Constructing geometric figures is a key part of mathematics. One of the simplest figures to construct is a square. A square has four equal sides and right angles at each corner. In this article, we will look at the steps to construct a square using different methods.
Introduction
The ability to construct geometric figures is essential for students, as it aids in developing spatial reasoning and visualization skills. Constructing a square is a basic but crucial skill that helps students understand the properties of squares and related geometric shapes.
What is a Square?
A square is a polygon with four equal sides and four 90degree angles. It is a regular polygon with four lines of symmetry. The diagonal of a square splits it into two congruent right triangles, and its length is the square root of two times the length of a side.
Constructing a Square with a Compass
Creating a square with a compass involves drawing circles and connecting their intersection points. Here are the steps for constructing a square using a compass:
 Draw a Line Segment: Draw a straight line segment of any length and label it AB.
 Draw the First Circle: Place the compass point on A and draw a circle with radius AB.
 Draw the Second Circle: Without changing the compass width, place the compass point on B and draw another circle that intersects the first circle at point C.
 Draw the Third Circle: Keeping the same compass width, place the compass point on C and draw a circle with radius AC.
 Draw the Fourth Circle: Again, without changing the compass width, place the compass point on A and draw another circle that intersects the previous circle at point D.
 Connect the Points: Draw straight lines connecting A to C, C to D, D to B, and B to A.
Constructing a Square in a Circle
Creating a square inside a circle involves drawing the square so that its corners touch the circle. Here’s a simple method to do this:

Draw a Circle: Draw a circle of any size and mark its center as point O.

Draw the Diameter: Draw a straight line through the center O, making the diameter of the circle. Label the endpoints of the diameter as A and B.

Draw a Perpendicular Diameter:
 Use a compass to draw another circle with the same radius as the first one. Place the pointed end on point A and draw a circle.
 Without changing the compass width, place the pointed end on point B and draw another circle intersecting the first circle. Label the intersection points as C and D.

Draw the Perpendicular Line: Draw a straight line through points C and D. This line should pass through the center O and is perpendicular to AB. Label the intersections of this line with the circle as points E and F.

Connect the Points: Draw straight lines connecting points A to E, E to B, B to F, and F to A.
Solved Example
Q. Construct a square with a side length of 5 cm using a compass and straightedge.
Solution:
 Draw a line segment AB using the straightedge.
 With the compass, draw a circle with center at point A and radius of 5 cm.
 Without changing the compass width, draw another circle with center at point B and intersecting the first circle at point C.
 Draw line segments AC and BC using the straightedge.
 Finally, draw line segments BD and AD to complete the square.
Now you have a square ABCD with side length of 5 cm.
Note that step 3 is crucial, as it ensures that points C and D are equidistant from both A and B, thus ensuring that the angles at C and D are both right angles, and that all four sides of the square are of equal length.
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Frequently Asked Questions on Construction of Square
Ans. To construct a square with a compass and straightedge, start by drawing a line segment. Use the compass to mark two equidistant points on the segment. These points become the square's vertices. Draw perpendicular lines from each vertex to the segment, forming right angles. Connect where these lines intersect the segment to complete the square.
Ans. A square has four sides of equal length.
Ans. A square's perimeter is equal to four times the length of one of its sides. Mathematically, P=4s, where P is the perimeter and s is the length of one side.