Before talking about the construction of quadrilaterals or special quadrilaterals, let us recall what a quadrilateral is. A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles.The sum of its interior angles is 360 degrees. A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, etc. are special types of quadrilaterals with some of their sides and angles being equal. In this article, we will discuss the construction of a special case of quadrilateral, that is, construction of square.
Steps for Construction of Square
A square is a quadrilateral with sides of equal length and angles of the same measure. Let us say you are required to construct a square. The only dimension provided is the length of one of its side, 5 cm. We know that the 4 interior angles of the square measure 90 degrees each. Hence, we do not require any other dimension for the construction of square. All the sides are equal in measurement and are perpendicular.
The steps of construction are as follows:
- Draw a line segment AB of 5 cm.
- Extend the line AB and using a compass, mark two arcs from B on the line. Mark the points as F and G.
- Mark arcs from point F and G above the line. The point where the arcs meet is named H.
- Join the point B and H.
- Set the compass to the radius of 5 cm and mark arc from points A and B. The point where the arc intersects BH is the vertex C of the square.
- With the same radius of 5 cm on the compass, mark an arc from the point C on the previously drawn arc above the point A. Mark their point of intersection as D.
- Join the points C and D as well as A and D to get the required square ABCD.
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