Construction of a rhombus
Let us learn how to construct a rhombus using the properties of its diagonals. (i.e) construction of a rhombus given two diagonals.
Example:
Construct a rhombus \(ABCD\) with diagonals \(8 \ cm\) and \(9 \ cm\).
Rough diagram:
In a rhombus, we know that the diagonals bisect each other.
\(BO = OD = \frac{9}{2} = 4.5 \ cm\)
\(AO = OC = \frac{8}{2} = 4 \ cm\)
Construction:
Step 1: Draw a line segment of length \(DB = 9 \ cm\).
Step 2: Mark a point \(O\) of line segment \(BD\) such that \(DO = OB = 4.5 \ cm\). At point \(O\), draw a perpendicular bisector using a protractor.
Step 3: With \(O\) as centre and \(4 \ cm\) as radius, draw two arcs on the perpendicular line and mark the intersections as \(A\) and \(C\), respectively.
Step 4: Join \(AD\), \(DC\), \(CB\) and \(BA\).
Thus, \(ABCD\) is the required rhombus.
Construction of a kite
Let us learn how to construct a kite when two diagonals are provided.
Example:
Construct a kite \(ABCD\) with diagonals \(AC = 10 \ cm\) and \(BD = 8 \ cm\).
Rough figure:
For kite \(ABCD\), diagonal \(AC\) bisects the diagonal \(BD\).
Thus, \(OB = OD = \frac{8}{2} = 4 \ cm\)
Also, the diagonals are perpendicular to each other.
\(\angle AOB = \angle BOC = \angle COD = \angle DOA = 90^{\circ}\)
Construction:
Step 1: Draw a line segment \(AC = 10 \ cm\).
Step 2: Mark a point \(O\) anywhere on the line segment \(AC\) and draw a perpendicular line to \(AC\) passing through \(O\).
Step 3: With \(O\) as the centre and \(4 \ cm\) as the radius, draw two arcs on the perpendicular line that intersect at \(B\) and \(D\).
Step 4: Join \(AB\), \(BC\), \(CD\) and \(DA\).
Thus, \(ABCD\) is the required kite.
Construction of an isosceles trapezium
Let us learn how to construct an isosceles trapezium in which the non-parallel sides are equal in length.
Example:
Construct an isosceles trapezium \(ABCD\) with \(AB \parallel CD\) and \(AB = 7 \ cm\) and \(AD = BC = 5 \ cm\).
Rough diagram:
Construction:
Step 1: Draw a line segment \(AB = 7 \ cm\).
Step 2: Draw a horizontal line parallel to \(AB\).
Step 3: With \(A\) and \(B\) as centres and a radius of \(5 \ cm\), draw an arc that cuts the horizontal line at \(D\) and \(C\), respectively.
Step 4: Join \(AD\) and \(BC\).
Thus, \(ABCD\) is the required isosceles trapezium.