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The perpendicular distances between the pairs of opposite sides of a parallelogram ABCD are 3 cm and 4 cm and one of its angles measures 60°. Using ruler and compasses only, construct ABCD.

Rectilinear Figures

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Answer

Steps of construction:

  1. Draw a straight-line PQ, take a point A on it.
  2. At A, construct ∠QAF = 60°
  3. At A, draw AE ⊥ PQ from AE cut off AN = 3 cm
  4. Through N draw a straight line to PQ to meet AF at D.
  5. At A, draw AG ⊥ AD, from AG cut off AM = 4 cm.
  6. Through M, draw a straight line parallel to AD to meet AQ at B and ND at C.
  7. Join AB, BC, CD and DA. Then, ABCD is the required parallelogram.
The perpendicular distances between the pairs of opposite sides of a parallelogram ABCD are 3 cm and 4 cm and one of its angles measures 60°. Using ruler and compasses only, construct ABCD. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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