Construction Of Parallelogram
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Construction of Parallelogram Example 1: Construct a parallelogram ABCD in which AB = 4m, BC = 3 cm and AC = 6 cm Solution:
Steps of construction 1. Draw AB = 4 cm, B as center draw an arc BC = 3 cm. Now A as center, draw an arc AC = 6 cm cutting the previous arc at C. Join AC and BC. 2. Now C as center and radius equal to 4 cm, draw an arc. 3. With A as center and radius equal to 3 cm, draw an arc cutting the previous arc at D. 4. Join AD and CD Now, ABCD is the required parallelogram. Example 2: Draw a parallelogram PQRS in which the diagonals are 4 cm and 6 cm. The angle between the diagonals is 60o Solution:
Steps of construction 1. Draw AC = 6 cm 2. Bisect AC at O. 3. Make an ∠60o at O and extend the arm on either side 4. Cut OD = OB = 2 cm 5. Join AB, BC, CD and DA
Now, ABCD is the required parallelogram Example 3: Construct a parallelogram PQRS in which PQ = 5 cm PS = 3 cm and ∠SPQ = 60o Solution:
Steps of construction 1. Draw PQ of length 5 cm 2. Make an angle of 60o at P. 3. P as center and radius = 3 cm cut PS = 3 cm 4. Now, Q as center and with the same radius, draw an arc. 5. S as center and radius = 5 cm, draw an arc cutting the previous arc at R. Join SR and QR. PQRS is the required parallelogram. Example 4: Draw a parallelogram ABCD in which AB = 5 cm, AD= 4 cm, and the distance between AB and CD is 3 cm Solution:
Steps of construction 1. Draw AB of length 5 cm 2. Make an angle of 90o at A. 3. Cut AE = 3 cm 4. Make an angle of 90o at E. 5. Cut AD = 4 cm 6. B as center and radius equal to 4 cm, draw an arc. 7. With D as center and radius equal to 5 cm, draw an arc cutting the previous arc at C. 8. Join BC and DC. ABCD is the required parallelogram
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Steps of construction 1. Draw AB = 4 cm, B as center draw an arc BC = 3 cm. Now A as center, draw an arc AC = 6 cm cutting the previous arc at C. Join AC and BC. 2. Now C as center and radius equal to 4 cm, draw an arc. 3. With A as center and radius equal to 3 cm, draw an arc cutting the previous arc at D. 4. Join AD and CD Now, ABCD is the required parallelogram. Example 2: Draw a parallelogram PQRS in which the diagonals are 4 cm and 6 cm. The angle between the diagonals is 60o Solution:
Steps of construction 1. Draw AC = 6 cm 2. Bisect AC at O. 3. Make an ∠60o at O and extend the arm on either side 4. Cut OD = OB = 2 cm 5. Join AB, BC, CD and DA
Now, ABCD is the required parallelogram Example 3: Construct a parallelogram PQRS in which PQ = 5 cm PS = 3 cm and ∠SPQ = 60o Solution:
Steps of construction 1. Draw PQ of length 5 cm 2. Make an angle of 60o at P. 3. P as center and radius = 3 cm cut PS = 3 cm 4. Now, Q as center and with the same radius, draw an arc. 5. S as center and radius = 5 cm, draw an arc cutting the previous arc at R. Join SR and QR. PQRS is the required parallelogram. Example 4: Draw a parallelogram ABCD in which AB = 5 cm, AD= 4 cm, and the distance between AB and CD is 3 cm Solution:
Steps of construction 1. Draw AB of length 5 cm 2. Make an angle of 90o at A. 3. Cut AE = 3 cm 4. Make an angle of 90o at E. 5. Cut AD = 4 cm 6. B as center and radius equal to 4 cm, draw an arc. 7. With D as center and radius equal to 5 cm, draw an arc cutting the previous arc at C. 8. Join BC and DC. ABCD is the required parallelogram
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