mark two points C and O , 3cm apart . construct a parallelogram CUBE, of center O nsuch that CU=8cm and CE=5cm. explane your construction
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Extend CO a further 3cm to create the line COB. This is one diagonal of the parallelogram. Using a pair of compasses set to 8cm, position the compasses at point C and draw an arc over the line segment OB. Set the compasses to 5cm, position the compasses at point B and draw an arc to cut the other arc. Where they intersect is point U. Position the compasses again at point C and describe an arc on the opposite side of line COB. Set the compasses to 8cm, position them at point B and describe an arc to cut through the other arc at point E. Join E to U and the line should pass through the centre O. This is the other diagonal, EOU. Finally join C to U, U to B, B to E and E to C to complete the parallelogram CUBE. Measure EO and OU, and you should find they're equal because the diagonals of a parallelogram bisect one another. The lines CU and EB should be parallel and length 8cm, and CE and BU should also be parallel of length 5cm.

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