Construct a parallelogram ABCD, if :
(i) AB = 3.6 cm, BC = 4.5 cm and ∠ABC=120∘.
(ii) BC = 4.5 cm, CD = 5.2 cm and ∠ADC=75∘.
(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.
(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.
(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75∘.
(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45∘.
(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is 60∘.
Construct a parallelogram ABCD, if :
(i) AB = 3.6 cm, BC = 4.5 cm and ∠ABC=120∘.
(ii) BC = 4.5 cm, CD = 5.2 cm and ∠ADC=75∘.
(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.
(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.
(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75∘.
(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45∘.
(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is 60∘.
(i) Rough figure is as follow :
The above rough figure is used to construct the actual || gm as follow :
Steps : 1. Draw AB = 3.6 cm.
2. Draw BP such that ∠B=120∘.
3. Cut BC = 4.5 cm.
4. From A, draw arc of radius 4.5 cm.
5. From C, draw arc of radius 3.6 cm. Which intersects first arc at D.
6. Join AD and CD.
Hence ABCD is the required || gm.
(ii) Rough figure is as follow :
∵ opposite sides of || gm are equal
∴ AD = BC = 4.5 cm.
∴ Actual construction is as follow :
Steps : 1. Draw CD = 5.2 cm.
2. Draw ∠CDP=75∘
3. Cut DA = 4.5 cm.
4. From A draw arc of radius 5.2 cm.
5. From C, draw arc of radius 4.5 cm which meets first arc at B.
6. Join AB and CB.
Thus ABCD is the required || gm.
(iii) Rough figure is as follow :
∵ opposite sides of || gm are equal
∴ AB = DC = 5 cm
Actual || gm is constructed as follow :
Steps : 1. Draw AD = 4 cm.
2. From A, draw an arc of radius 5 cm.
3. From D, draw an arc of radius 7 cm which intersects first arc at B.
4. From B, draw an arc of radius 4 cm.
5. From D, draw an arc of radius 5 cm which intersect first arc at C.
6. Join AB, BD, BC and CD.
Thus ABCD is the required || gm.
(iv) Rough figure is as follow :
opposite sides of || gm are equal
∴ BC = AD = 4.6 cm.
Actual figure is constructed as follow :
Steps : 1. Draw AB = 5.8 cm.
2. Draw an arc of radius 4.6 cm with centre B.
3. Draw an arc of radius 7.5 cm from A which intersects first arc at C.
4. From A, draw an arc of radius 4.6 cm.
5. From C, draw an arc of radius 5.8 cm which intersects first arc at D.
6. Join AD, CD, BC and AC.
Thus ABCD is the required || gm.
(v) Rough figure is as follow.
∵ Diagonals of || gm bisect each other.
∴ OB = OD = 12BD=2.8 cm.
Actual figure is constructed with the help of above figure as follow.
Steps :
1. Draw AC = 6.4 cm.
2. Bisect AC at O.
3. Draw ∠XOC=75∘ and produce XO to Y.
4. Cut OB = OD = 2.8 cm.
5. Join AB, BC, AD and CD.
Thus ABCD is the required || gm.
(vi)
Steps :
1. Draw AC = 6.3 cm.
2. Bisect AC at O.
3. At O, draw ∠XOC=45∘ and produce XO to Y.
4. Cut OB = OD = 3.5 cm (half the diagonal 7 cm.)
5. Join AB, CB, AD and CD. Thus ABCD is the required || gm.
(vii)
Steps :
1. Draw BD = 6.7 cm.
2. Bisect BD at O.
3. At O, draw ∠XOD=60∘. and produce XO to Y.
4. Cut OA = OC = 2.7 cm
(half the diagonals 5.4 cm)
5. Join AB, AD, BC and CD.
Thus ABCD is the required || gm.
(i) Rough figure is as follow :
The above rough figure is used to construct the actual || gm as follow :
Steps : 1. Draw AB = 3.6 cm.
2. Draw BP such that ∠B=120∘.
3. Cut BC = 4.5 cm.
4. From A, draw arc of radius 4.5 cm.
5. From C, draw arc of radius 3.6 cm. Which intersects first arc at D.
6. Join AD and CD.
Hence ABCD is the required || gm.
(ii) Rough figure is as follow :
∵ opposite sides of || gm are equal
∴ AD = BC = 4.5 cm.
∴ Actual construction is as follow :
Steps : 1. Draw CD = 5.2 cm.
2. Draw ∠CDP=75∘
3. Cut DA = 4.5 cm.
4. From A draw arc of radius 5.2 cm.
5. From C, draw arc of radius 4.5 cm which meets first arc at B.
6. Join AB and CB.
Thus ABCD is the required || gm.
(iii) Rough figure is as follow :
∵ opposite sides of || gm are equal
∴ AB = DC = 5 cm
Actual || gm is constructed as follow :
Steps : 1. Draw AD = 4 cm.
2. From A, draw an arc of radius 5 cm.
3. From D, draw an arc of radius 7 cm which intersects first arc at B.
4. From B, draw an arc of radius 4 cm.
5. From D, draw an arc of radius 5 cm which intersect first arc at C.
6. Join AB, BD, BC and CD.
Thus ABCD is the required || gm.
(iv) Rough figure is as follow :
opposite sides of || gm are equal
∴ BC = AD = 4.6 cm.
Actual figure is constructed as follow :
Steps : 1. Draw AB = 5.8 cm.
2. Draw an arc of radius 4.6 cm with centre B.
3. Draw an arc of radius 7.5 cm from A which intersects first arc at C.
4. From A, draw an arc of radius 4.6 cm.
5. From C, draw an arc of radius 5.8 cm which intersects first arc at D.
6. Join AD, CD, BC and AC.
Thus ABCD is the required || gm.
(v) Rough figure is as follow.
∵ Diagonals of || gm bisect each other.
∴ OB = OD = 12BD=2.8 cm.
Actual figure is constructed with the help of above figure as follow.
Steps :
1. Draw AC = 6.4 cm.
2. Bisect AC at O.
3. Draw ∠XOC=75∘ and produce XO to Y.
4. Cut OB = OD = 2.8 cm.
5. Join AB, BC, AD and CD.
Thus ABCD is the required || gm.
(vi)
Steps :
1. Draw AC = 6.3 cm.
2. Bisect AC at O.
3. At O, draw ∠XOC=45∘ and produce XO to Y.
4. Cut OB = OD = 3.5 cm (half the diagonal 7 cm.)
5. Join AB, CB, AD and CD. Thus ABCD is the required || gm.
(vii)
Steps :
1. Draw BD = 6.7 cm.
2. Bisect BD at O.
3. At O, draw ∠XOD=60∘. and produce XO to Y.
4. Cut OA = OC = 2.7 cm
(half the diagonals 5.4 cm)
5. Join AB, AD, BC and CD.
Thus ABCD is the required || gm.
