Rectilinear Figures


   
 
Construction of Special types of Quadrilaterals
Construction of Parallelograms
 
(a) Two sides and an angle are given
 
 
AB = 5 cm, BC = 3.3 cm and ÐA = 60o
 
 
 
(i) Draw AB = 5 cm and make ÐA = 60o
 
(ii) Cut AD = 3.3 cm (AD = BC)
 
(iii) With B as centre and radius 3.3 cm, draw one arc and with D as centre and radius 5 cm cut that arc at C.
 
(iv) Join BC and DC.
 
Then ABCD is the required parallelogram.
 
(b) Diagonals and the angle included by them are given
 
 
AC = 7 cm, BD = 6 cm and the angle included by them is 60o.
 
 
(i) AC = 7 cm and draw its perpendicular bisector to get mid-point O.
 
(ii) At O make ÐCOX = 60o and produce it both ways.
 
(iii) With O as centre and radius 3 cm cut OX at D and B.
 
(iv) Join AB, BC, CD and AD.
 
Then ABCD is the required parallelogram.
 
 
(c) One side, diagonal and height are given
 
 
AB = 4cm, height = 2.5 cm and AC = 3.5 cm
 
 
(i) Draw AB = 4 cm.
 
(ii) Draw AX AB and on AX mark E such that AE = 2.5 cm.
 
(iii) Through E draw PQ || AB.
 
(iv) With A as centre and radius 3.5 cm cut PQ at C.
 
(v) With C as centre and radius 4 cm cut CD = 4 cm.
 
(vi) Join BC, AD.
 
Then ABCD is the required parallelogram.
 
 
Construction of a Rhombus
 
(a) Both the diagonals are given
 
 
AC = 6 cm, BD = 4.5 cm
 
 
(i) Draw BD = 4.5 cm.
 
(ii) Construct the perpendicular bisector XY at O.
 
(iii) With O as centre and radius 3 cm.
 
(=) cut XY at A and C.
 
(iv) Join AB, BC, CD and AD.
 
Then ABCD is the required rhombus.
 
 
(b) One diagonal and one side are given
 
 
AC = 6.5 cm and AB = 3.8 cm
 
 
(i) Draw AC = 6.5 cm.
 
(ii) With A as centre and radius 3.8 cm, draw arcs on either side of AC.
 
(iii) With centre C and the same radius of 3.8 cm, cut these arcs at B and D.
 
(iv) Join AB, BC, CD and AD.
 
Then ABCD is the required rhombus.
 
 
Construction of a Square
 
Diagonals are given
 
 
AC = 5.2 cm
 
 
In a square diagonals are equal.
 
 
(i) Draw AC = 5.2 cm.
 
(ii) Construct XY which bisects AC at O.
 
(iii) With centre O and radius 2.6 cm ((=BD), cut XY at D and B.
 
(iv) Join AB, BC, CD and AD.
 
(v) \ABCD is the required square.
 
 
Construction of a Rectangle
 
 
Diagonal and the angle included by them are given.
 
 
A Rectangle ABCD, given AC = 7cm, BC = 7 cm and the angle included by them is 60o.
 
 
 
(i) Draw AC = 7 cm.
 
(ii) Construct its perpendicular bisector to obtain the midpoint O.
 
(iii) At O, construct ÐCOX = 60o and produce it both ways.
 
(iv) With O as centre and radius 3.5 cm, cut OX at D and B.
 
(v) Join AB, BC, CD and AD.
 
(vi) \ ABCD is the required rectangle.
 
  
     
   
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