Construction of a rectangle
Let us construct a rectangle when the diagonals and their intersection angles are known.
Example:
Construct a rectangle whose diagonals have equal lengths of \(10 \ cm\) that bisect each other, and intersect at an angle of \(50^{\circ}\).
Construction:
Step 1: Draw a line segment of length \(AC = 10 \ cm\).
Step 2: Mark the midpoint of the line segment as \(O\).
Step 3: Place the protractor at O. Draw a line through \(O\) making an angle of \(50°\) with \(AC\).
Step 4: With \(O\) as the centre, and \(5 \ cm\) as the radius draw arcs on both sides of the newly drawn line and mark them as \(B\) and \(D\).
Step 5: Join \(AB\), \(BC\), \(CD\) and \(DA\).
Therefore, \(ABCD\) is the required rectangle.
Construction of a square
Let us construct a square when its diagonals are known.
Example:
Construct a square with one of its diagonals as \(10\) \(cm\).
Construction:
Step 1: Draw a line segment \(AC\) of length \(10\) \(cm\).
Step 2: Draw a perpendicular bisector to \(AC\) such that the bisector intersects \(AC\) at \(O\).
Step 3: With \(O\) as the centre and with \(5\) \(cm\) as the radius, draw arcs on both sides of the perpendicular bisector. Mark the intersections as \(B\) and \(D\).
Step 4: Join \(AB\), \(BC\), \(CD\), and \(AD\) to form the desired square.
Thus, \(ABCD\) is the required square.
Construction of a parallelogram
Let us learn how to construct a parallelogram when two adjacent sides and an angle between them are provided.
Example:
Construct a parallelogram \(ABCD\) with \(AB = 6 \ cm\), \(BC = 5.5 \ cm\) and \(\angle ABC = 75^{\circ}\).
Construction:
Step 1: Draw a line segment \(AB = 6 \ cm\).
Step 2: With \(B\) as centre, mark an angle \(75^{\circ}\) using the protractor and mark it as \(X\). Join \(BX\).
Step 3: With \(B\) as centre, draw an arc of radius \(5.5 \ cm\) intersecting \(BX\) at \(C\).
Step 4: With \(C\) and \(A\) as centres, draw two arcs of radii \(6 \ cm\) and \(5.5 \ cm\), respectively such that they intersect each other at \(D\).
Step 5: Join \(AD\) and \(CD\).
Thus, \(ABCD\) is the required parallelogram.