Construction of Special types of Quadrilaterals

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Construction of Parallelograms

(a) Two sides and an angle are given

AB = 5 cm, BC = 3.3 cm and ÐA = 60^o

(i) Draw AB = 5 cm and make ÐA = 60^o

(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 60^o.

(i) AC = 7 cm and draw its perpendicular bisector to get mid-point O.

(ii) At O make ÐCOX = 60^o 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 60^o.

(i) Draw AC = 7 cm.

(ii) Construct its perpendicular bisector to obtain the midpoint O.

(iii) At O, construct ÐCOX = 60^o 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.