The construction of square, rectangle, rhombus, parallelogram and trapezium are explained below:
construction square
Here, ABCD is a square where AB = 8 cm.
Step 1: Draw AB = 8 cm.
Step 2: Construct angle 90^{0} at both A and B.
Step 3: Cut AX at 8 cm from A and name it D. Similarly, cut BY at 8 cm from B and name it C.
Step 4: Join C and D.
Therefore, a square ABCD having a side 8 cm is formed.
Here, MNOP is a square whose diagonal NP = 5 cm.
Step 1: Draw NP = 5 cm.
Step 2: Draw 45^{0} angles at N and P.
Step 3: NX and PY intersect at M.
Step 4: Take an arc equal to MN or MP and draw two arcs downwards such that they intersect at C.
Step 5: Now, join N,O and P,O.
Therefore, a square MNOP having a diagonal NP = 5 cm is formed.
Here, ABCD is a rectangle in which BC = 5 cm and AB = 4 cm.
Step 1: Draw BC = 5 cm.
Step 2: Construct 90^{0} angles at both points A and B.
Step 3: Take an arc of 4 cm and cut the BX at A and CY at D.
Step 4: Join A and B.
Therefore, a rectangle ABCD having BC = 5 cm and AB = 4 cm is formed.
Here, ABCD is a rectangle in which AC = BD = 5 cm and an angle = 45^{0}.
Step 1: Draw AC = 5 cm.
Step 2: Find the mid-point O of the line AC with the help of perpendicular bisector method.
Step 3: Construct 45^{0} angle at O. Produce the line XO straight upto Y on other side.
Step 4: Take an arc of 2.5 cm and cut OX at D and OY at B.
Step 5: Join A and B, B and C, C and D, D and A.
Therefore, a rectangle ABCD having AC = BD = 5 cm and an angle = 45^{0} is formed.
Here, a rhombus MNOP with side MN = 5 cm and∠NMP = 60^{0}.
Step 1: Draw MN = 5 cm.
Step 2: Draw ∠NMX = 60^{0} at M.
Step 3: Take measure of 5 cm and cut MX at P.
Step 4: Take a radius of 5 cm from N and P, draw two arcs such that they intersect at O.
Step 5: Join P and O, O and N.
Therefore, a rhombus MNOP is formed.
Here, a rhombus ABCD having diagonal AC = 5 cm and BD = 6 cm.
Step 1: Draw the diagonal AC = 5 cm.
Step 2: Draw the perpendicular bisector XY of AC such that the mid-point is O.
Step 3: Take radius of 3 cm (half of diagonal BD) and from O, cut OY at D and OX at B.
Step 4: Joint A and B, B and C, C and D, D and A.
Therefore, a rhombus ABCD is formed.
Here, a rhombus ABCD where AB = 6 cm and AC = 8 cm.
Step 1: Draw AB = 6 cm.
Step 2: Keeping A center, take an arc of 8 cm.
Step 3: From B, take an arc of 6 cm and cut the previous arc and name it C.
Step 4: Join B and C, A and D.
Step 5: Again, taking A as centre, draw an arc of 5.5 cm upright and take another same arc from C and cut the previous arc and name it.
Step 6: Join C and D, D and A.
Therefore, a rhombus ABCD is formed.
Here, a parallelogram ABCD in which BC = 6 cm, CD = 5 cm and∠BCD = 120^{0}.
Step 1: Draw BC = 6 cm.
Step 2: Construct an angle of 120^{0} at C, i.e.∠BCX = 120^{0}.
Step 3: Take an arc of 4.5 cm and cut CX at D.
Step 4: With centre at B, draw an arc upright with radius of 4.5 cm.
Step 5: Likewise, with centre at D, draw another arc with radius of 5 cm.
Step 6: Join A and D, A and B.
Therefore, a parallelogram ABCD is formed.
Here, a parallelogram MNOP where base MN = 6 cm, diagonal MO = 8 cm and∠NMO = 30^{0}.
Step 1: Draw MN = 6 cm.
Step 2: Construct an angle of 30^{0} at M (i.e. ∠NMX = 30^{0}).
Step 3: Take a radius of 8 cm and cut MX at O from M.
Step 4: Join N and O.
Step 5: With centre at O, take radius of 6 cm and draw an arc.
Step 6: Likewise with centre at M, take a radius equal to NO and cut the previous arc. Name the intersecting points as P.
Step 7: Join O and P, P and M.
Therefore, a reqiured parallelogram MNOP is formed.
Here, PQ = 6 cm and diagonals PR = 9 cm and QS = 6.5 cm.
Step 1: Draw a base line PQ = 6 cm.
Step 2: Take a radius of 5 cm and draw an arc up from point P.
Step 3: Similarly, take a radius of 5 cm and draw an arc up from Q. Such that it meets the previous arc. Name the point O.
Step 4: Join the point O to P and Q.
Step 5: Produce PO to R such that PO = OR. And produce QO to S such that QO =OS.
Step 6: Join P and S, S and R, R and Q.
Therefore, the required parallelogram PQRS is formed.
Here, PR = 6 cm, QS = 8 cm and angle between these two diagonals is 45^{0}.
Step 1: Draw PR = 6 cm.
Step 2: Draw the bisector of PR and find the mid-point O.
Step 3: At O, draw an angle of 45^{0}.
Step 4: Take a radius of 4 cm (half of QS) and cut OX at S and OY at Q.
Step 5: Join P and Q, Q and R, R and S, S and P.
Therefore, the required parallelogram PQRS is formed.
Here, AB = 6 cm, BC = 5 cm, ∠DAB = 60^{0}, ∠BCD = 90^{0} and AD||BC.
Step 1: Draw a base line AB = 6 cm.
Step 2: Construct an angle of ∠BAX =60^{0}.
Step 3: Since, BC||AD, the angle at B should be 120^{0}. So, construct an angle of 120^{0}. (i.e. ∠ABY = 120^{0}).
Step 4: Taking a radius of 5 cm, mark the point C on BY from the point B.
Step 5: Construct an angle of 90^{0}at C. Thus formed line CD meets the pervious line AX at D.
Therefore, the required trapezium ABCD is formed.
Here, AB = 6 cm, diagonal BD = 8 cm, ∠BAD = 60^{0}.
Step 1: Draw a base line AB = 6 cm.
Step 2: Construct an angle of 60^{0} (i.e. ∠BAX) at A.
Step 3: Taking a radius of 8 cm, mark the point D on AX from Q.
Step 4: Join B and D.
Step 5: Since AB||CD, alternate angles are equal. So, construct an angle of 60^{0} at C with base AC to make an equal alternate∠XDC.
Step 6: Take a radius of 7 cm and from point D draw an arc to cut DY at C.
Step 7: Join C and B.
Therefore, the required trapezium ABCD is formed.
Here, PE = 8 cm, diagonal ET = 6 cm, TU = 4 cm and ∠PET = 60^{0} such that PE||TU.
Step 1: Draw a base line segment PE = 8 cm.
Step 2: Draw an angle∠PEX = 60^{0} at point E.
Step 3: Taking an arc of 6 cm from E, mark point T on EX.
Step 4: At point T, draw an∠ETY = 120^{0}.
Step 5: Taking an arc of 4 cm from T, mark point U on TY.
Step 6: Join U and P.
Therefore, the required trapezium PETU is formed where PE||TU.
ASK ANY QUESTION ON Construction
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Mar 06, 2017
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sirish chaudhary
construction of parallelogram where height and base are given
Mar 05, 2017
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nirpa bk
Ask any queries on this note.when given the hheight of parallogram
Mar 05, 2017
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Parallelogram
Construction of parallelogram
Feb 07, 2017
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