Before talking about the construction of 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 a special case of the construction of rhombus, where the measurement of its two diagonals is given.
Construction of Rhombus
A rhombus is a quadrilateral with sides of equal length. Opposite sides are parallel and opposite vertex angles are equal. Let us say, you are required to construct a rhombus PQRS with the lengths of its two diagonals, PR = 6 cm and SQ = 7 cm. We know that the diagonals of a rhombus bisect each other at 90 degrees. Hence, we do not require any other dimension for the construction of rhombus. The steps are:
- Draw a vertical line segment PR of length 6 cm.
- Take the compass of any radius and from the point P, mark an arc towards the left and the other towards the right of PR. Repeat the same from the point R without changing the compass radius.
- The other diagonal measures 7 cm. Thus, draw a line joining the two points where the arc intersected each other in such a way that OS = OQ = 7/2 = 3.5 cm
- Join the point P with Q, Q with R, R with S and S with P.
PQRS is the required rhombus with the diagonals of lengths 6 cm and 7 cm. Note that O is the mid-point of the two diagonals and ∠POQ = ∠QOR = ∠ROS = ∠SOP = 90 degrees.
To learn more about rhombus, click on the linked article.