Mathematics
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:
- Draw a straight-line PQ, take a point A on it.
- At A, construct ∠QAF = 60°
- At A, draw AE ⊥ PQ from AE cut off AN = 3 cm
- Through N draw a straight line to PQ to meet AF at D.
- At A, draw AG ⊥ AD, from AG cut off AM = 4 cm.
- Through M, draw a straight line parallel to AD to meet AQ at B and ND at C.
- Join AB, BC, CD and DA. Then, ABCD is the required parallelogram.
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